prob
prob,
an Octave code which
handles various discrete and
continuous probability density functions
(PDF).
For a discrete variable X, PDF(X) is the probability that the value
X will occur; for a continuous variable, PDF(X) is the probability
density of X, that is, the probability of a value between X and X+dX
is PDF(X) * dX.
The corresponding cumulative density functions or "CDF"'s are also
handled. For a discrete or continuous variable, CDF(X) is the
probability that the variable takes on a value less than or equal to X.
In some cases, the inverse of the CDF can easily be computed.
If
X = CDF_INV ( P )
then we are asserting that the value X has a cumulative
probability density function of P, in other words,
the probability that the variable is less than or equal to X
is P. If the CDF cannot be analytically inverted, there
are simple ways to try to estimate the inverse. Depending on
the PDF, these methods may be rapid and accurate, or not.
For most distributions, the mean or "average value" or
"expected value" is also available. For a discrete variable, MEAN
is simply the sum of the products X * PDF(X); for a continuous
variable, MEAN is the integral of X * PDF(X) over the range.
For the distributions covered here, the means are known beforehand,
and no summation or integration is required.
For most distributions, the variance is available. For a
discrete variable, the variance is the sum of the products
( X - MEAN )^2 * PDF(X); for a continuous variable, the
variance is the integral of ( X - MEAN )^2 * PDF(X) over the range.
The square root of the variance is known as the standard
deviation. For the distributions covered here, the variances are
often known beforehand, and no summation or integration is required.
For many of the distributions, it is possible to repeatedly
request "samples", that is, a pseudorandom sequence of realizations
of the PDF. These samples are always associated with an integer
seed, which controls the calculation. Using the same seed as input
will guarantee the same sample value on output. Ultimately, a
random number generator must be invoked internally. In most cases,
the current code will call a routine called r8_uniform_ab() or
i4_uniform_ab(), each of which in turn calls a routine called
r8_uniform_01(). You may prefer a different random number generator
for this purpose.
Licensing:
The information on this web page is distributed under the MIT license.
Languages:
prob is available in
a C version and
a C++ version and
a Fortran77 version and
a Fortran90 version and
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
prob_test
test_values,
an Octave code which
contains sample values for a number of distributions.
Source Code:
-
angle_cdf.m
evaluates the Angle CDF.
-
angle_mean.m
returns the mean of the Angle PDF.
-
angle_pdf.m
evaluates the Angle PDF.
-
anglit_cdf.m
evaluates the Anglit CDF.
-
anglit_cdf_inv.m
inverts the Anglit CDF.
-
anglit_mean.m
returns the mean of the Anglit PDF.
-
anglit_pdf.m
evaluates the Anglit PDF.
-
anglit_sample.m
samples the Anglit PDF.
-
anglit_variance.m
returns the variance of the Anglit PDF.
-
arcsin_cdf.m
evaluates the Arcsin CDF.
-
arcsin_check.m
checks the parameters of the Arcsin PDF.
-
arcsin_cdf_inv.m
inverts the Arcsin CDF.
-
arcsin_mean.m
returns the mean of the Arcsin PDF.
-
arcsin_pdf.m
evaluates the Arcsin PDF.
-
arcsin_sample.m
samples the Arcsin PDF.
-
arcsin_variance.m
returns the variance of the Arcsin PDF.
-
benford_cdf.m
returns the Benford CDF.
-
benford_cdf_inv.m
returns the Benford CDF.
-
benford_mean.m
returns the mean of the Benford PDF.
-
benford_pdf.m
returns the Benford probability of one or more significant digits.
-
benford_sample.m
samples the Benford PDF.
-
benford_variance.m
returns the variance of the Benford PDF.
-
bernoulli_cdf.m
evaluates the Bernoulli CDF.
-
bernoulli_cdf_inv.m
inverts the Bernoulli CDF.
-
bernoulli_check.m
checks the parameter of the Bernoulli CDF.
-
bernoulli_mean.m
returns the mean of the Bernoulli PDF.
-
bernoulli_pdf.m
evaluates the Bernoulli PDF.
-
bernoulli_sample.m
samples the Bernoulli PDF.
-
bernoulli_variance.m
returns the variance of the Bernoulli PDF.
-
bessel_i0.m
evaluates the Bessel function I0(x).
-
bessel_i0_values.m
returns some values of the Bessel function I0(x).
-
bessel_i1.m
evaluates the Bessel function I1(x).
-
bessel_i1_values.m
returns some values of the Bessel function I1(x).
-
bessel_ix_values.m
returns some values of the Bessel function In(x)
for noninteger order.
-
beta_binomial_cdf.m
evaluates the Beta Binomial CDF.
-
beta_binomial_cdf_inv.m
inverts the Beta Binomial CDF.
-
beta_binomial_check.m
checks the parameters of the Beta Binomial PDF.
-
beta_binomial_mean.m
returns the mean of the Beta Binomial PDF.
-
beta_binomial_pdf.m
evaluates the Beta Binomial PDF.
-
beta_binomial_sample.m
samples the Beta Binomial CDF.
-
beta_binomial_variance.m
returns the variance of the Beta Binomial PDF.
-
beta_cdf.m
evaluates the Beta CDF.
-
beta_cddf_inv.m
inverts the Beta CDF.
-
beta_cdf_values.m
returns some values of the Beta CDF.
-
beta_check.m
checks the parameters of the Beta PDF.
-
beta_inc.m
returns the value of the incomplete Beta function.
-
beta_inc_values.m
returns some values of the incomplete Beta function.
-
beta_mean.m
returns the mean of the Beta PDF.
-
beta_pdf.m
evaluates the Beta PDF.
-
beta_sample.m
samples the Beta PDF.
-
beta_values.m
returns selected values of the Beta function.
-
beta_variance.m
returns the variance of the Beta PDF.
-
binomial_cdf.m
evaluates the Binomial CDF.
-
binomial_cdf_inv.m
inverts the Binomial CDF.
-
binomial_cdf_values.m
returns some values of the Binomial CDF.
-
binomial_check.m
checks the parameter of the Binomial PDF.
-
binomial_coef.m
computes the Binomial coefficient C(N,K).
-
binomial_coef_log.m
computes the logarithm of the Binomial coefficient.
-
binomial_mean.m
returns the mean of the Binomial PDF.
-
binomial_pdf.m
evaluates the Binomial PDF.
-
binomial_sample.m
samples the Binomial PDF.
-
binomial_variance.m
returns the variance of the Binomial PDF.
-
birthday_cdf.m
evaluates the Birthday CDF.
-
birthday_cdf_inv.m
inverts the Birthday CDF.
-
birthday_pdf.m
evaluates the Birthday PDF.
-
birthday_sample.m
samples the Birthday distribution.
-
bradford_cdf.m
evaluates the Bradford CDF.
-
bradford_cdf_inv.m
inverts the Bradford CDF.
-
bradford_check.m
checks the parameters of the Bradford PDF.
-
bradford_mean.m
returns the mean of the Bradford PDF.
-
bradford_pdf.m
evaluates the Bradford PDF.
-
bradford_sample.m
samples the Bradford PDF.
-
bradford_variance.m
returns the variance of the Bradford PDF.
-
buffon_box_pdf.m
evaluates the Buffon Box PDF.
-
buffon_box_sample.m
simulates the Buffon Box needle experiment.
-
buffon_pdf.m
evaluates the Buffon PDF.
-
buffon_sample.m
simulates the Buffon needle experiment.
-
burr_cdf.m
evaluates the Burr CDF.
-
burr_cdf_inv.m
inverts the Burr CDF.
-
burr_check.m
checks the parameters of the Burr CDF.
-
burr_mean.m
returns the mean of the Burr PDF.
-
burr_pdf.m
evaluates the Burr PDF.
-
burr_sample.m
samples the Burr PDF.
-
burr_variance.m
returns the variance of the Burr PDF.
-
c_normal_01_sample.m
samples the complex Normal 01 PDF.
-
cardioid_cdf.m
evaluates the Cardioid CDF.
-
cardioid_cdf_inv.m
inverts the Cardioid CDF.
-
cardioid_check.m
checks the parameters of the Cardioid CDF.
-
cardioid_mean.m
returns the mean of the Cardioid CDF.
-
cardioid_pdf.m
evaluates the Cardioid PDF.
-
cardioid_sample.m
samples the Cardioid CDF.
-
cardioid_variance.m
returns the variance of the Cardioid CDF.
-
cauchy_cdf.m
evaluates the Cauchy CDF.
-
cauchy_cdf_inv.m
inverts the Cauchy CDF.
-
cauchy_cdf_values.m
returns some values of the Cauchy CDF.
-
cauchy_check.m
checks the parameters of the Cauchy CDF.
-
cauchy_mode.m
returns the mode of the Cauchy PDF.
-
cauchy_pdf.m
evaluates the Cauchy PDF.
-
cauchy_sample.m
samples the Cauchy PDF.
-
chebyshev1_cdf.m
evaluates the Chebyshev1 CDF.
-
chebyshev1_cdf_inv.m
inverts the Chebyshev1 CDF.
-
chebyshev1_mean.m
returns the mean of the Chebyshev1 PDF.
-
chebyshev1_pdf.m
evaluates the Chebyshev1 PDF.
-
chebyshev1_sample.m
samples the Chebyshev1 PDF.
-
chebyshev1_variance.m
returns the variance of the Chebyshev1 PDF.
-
chebyshev2_pdf.m
evaluates the Chebyshev2 PDF.
-
chi_cdf.m
evaluates the Chi CDF.
-
chi_cdf_inv.m
inverts the Chi CDF.
-
chi_check.m
checks the parameters of the Chi CDF.
-
chi_mean.m
returns the mean of the Chi PDF.
-
chi_pdf.m
evaluates the Chi PDF.
-
chi_sample.m
samples the Chi PDF.
-
chi_variance.m
returns the variance of the Chi PDF.
-
chi_square_cdf.m
evaluates the chi-squared CDF.
-
chi_square_cdf_inv.m
inverts the chi-squared PDF.
-
chi_square_cdf_values.m
returns values of the Chi-Square central CDF.
-
chi_square_check.m
checks the parameter of the central Chi-Squared PDF.
-
chi_square_mean.m
returns the mean of the central Chi-Squared PDF.
-
chi_square_pdf.m
evaluates the central Chi-Squared PDF.
-
chi_square_sample.m
samples the central Chisquare PDF.
-
chi_square_variance.m
returns the variance of the central Chisquare PDF.
-
chi_square_noncentral_check.m
checks the parameters of the noncentral Chi-Squared PDF.
-
chi_square_noncentral_cdf_values.m
returns some values of the noncentral Chi-Squared CDF.
-
chi_square_noncentral_mean.m
returns the mean of the noncentral Chi-Squared PDF.
-
chi_square_noncentral_sample.m
samples the noncentral Chisquare PDF.
-
chi_square_noncentral_variance.m
returns the variance of the noncentral Chi-Squared PDF.
-
circular_normal_01_mean.m
returns the mean of the Circular Normal 01 PDF.
-
circular_normal_01_pdf.m
evaluates the Circular Normal 01 PDF.
-
circular_normal_01_sample.m
samples the Circular Normal 01 PDF.
-
circular_normal_01_variance.m
returns the variance of the Circular Normal 01 PDF.
-
circular_normal_mean.m
returns the mean of the Circular Normal PDF.
-
circular_normal_pdf.m
evaluates the Circular Normal PDF.
-
circular_normal_sample.m
samples the Circular Normal PDF.
-
circular_normal_variance.m
returns the variance of the Circular Normal PDF.
-
cosine_cdf.m
evaluates the Cosine CDF.
-
cosine_cdf.m
inverts the Cosine CDF.
-
cosine_check.m
checks the parameters of the Cosine CDF.
-
cosine_mean.m
returns the mean of the Cosine PDF.
-
cosine_pdf.m
evaluates the Cosine PDF.
-
cosine_sample.m
samples the Cosine PDF.
-
cosine_variance.m
returns the variance of the Cosine PDF.
-
coupon_complete_pdf.m
evaluates the Coupon Complete PDF.
-
coupon_mean.m
returns the variance of the Coupon PDF.
-
coupon_sample.m
samples the Coupon PDF.
-
coupon_variance.m
returns the variance of the Coupon PDF.
-
deranged_cdf.m
evaluates the Deranged CDF.
-
deranged_cdf_inv.m
inverts the Deranged CDF.
-
deranged_check.m
checks the parameter of the Deranged PDF.
-
deranged_enum.m
returns the number of derangements of N objects.
-
deranged_mean.m
returns the mean of the Deranged CDF.
-
deranged_pdf.m
evaluates the Deranged PDF.
-
deranged_sample.m
samples the Deranged PDF.
-
deranged_variance.m
returns the variance of the Deranged CDF.
-
digamma.m
calculates the digamma or Psi function
= d ( LOG ( GAMMA ( X ) ) ) / dX
-
dipole_cdf.m
evaluates the Dipole CDF.
-
dipole_cdf_inv.m
inverts the Dipole CDF.
-
dipole_check.m
checks the parameters of the Dipole CDF.
-
dipole_pdf.m
evaluates the Dipole PDF.
-
dipole_sample.m
samples the Dipole PDF.
-
dirichlet_check.m
checks the parameters of the Dirichlet PDF.
-
dirichlet_mean.m
returns the means of the Dirichlet PDF.
-
dirichlet_moment2.m
returns the second moments of the Dirichlet PDF.
-
dirichlet_pdf.m
evaluates the Dirichlet PDF.
-
dirichlet_sample.m
samples the Dirichlet PDF.
-
dirichlet_variance.m
returns the variances of the Dirichlet PDF.
-
dirichlet_mix_check.m
checks the parameters of a Dirichlet Mix PDF.
-
dirichlet_mix_mean.m
returns the means of a Dirichlet Mix PDF.
-
dirichlet_mix_pdf.m
evaluates a Dirichlet Mix PDF.
-
dirichlet_mix_sample.m
samples a Dirichlet Mix PDF.
-
dirichlet_multinomial_pdf.m
evaluates a Dirichlet Multinomial PDF.
-
discrete_cdf.m
evaluates the Discrete CDF.
-
discrete_cdf_inv.m
inverts the Discrete CDF.
-
discrete_check.m
checks the parameters of the Discrete CDF.
-
discrete_mean.m
evaluates the mean of the Discrete PDF.
-
discrete_pdf.m
evaluates the Discrete PDF.
-
discrete_sample.m
samples the Discrete PDF.
-
discrete_variance.m
evaluates the variance of the Discrete PDF.
-
disk_mean.m
mean of points in a disk.
-
disk_sample.m
sample points in a disk.
-
disk_variance.m
variance of points in a disk.
-
e_constant.m
returns the value of E.
-
empirical_discrete_cdf.m
evaluates the Empirical Discrete CDF.
-
empirical_discrete_cdf_inv.m
inverts the Empirical Discrete CDF.
-
empirical_discrete_check.m
checks the parameters of the Empirical Discrete CDF.
-
empirical_discrete_mean.m
returns the mean of the Empirical Discrete PDF.
-
empirical_discrete_pdf.m
evaluates the Empirical Discrete PDF.
-
empirical_discrete_sample.m
samples the Empirical Discrete PDF.
-
empirical_discrete_variance.m
returns the variance of the Empirical Discrete PDF.
-
english_letter_cdf.m
evaluates the English Letter CDF.
-
english_letter_cdf_inv.m
inverts the English Letter CDF.
-
english_letter_pdf.m
evaluates the English Letter PDF.
-
english_letter_sample.m
samples the English Letter CDF.
-
english_sentence_length_cdf.m
evaluates the English Sentence Length CDF.
-
english_sentence_length_cdf_inv.m
inverts the English Sentence Length CDF.
-
english_sentence_length_mean.m
evaluates the mean of the English Sentence Length PDF.
-
english_sentence_length_pdf.m
evaluates the English Sentence Length PDF.
-
english_sentence_length_sample.m
samples the English Sentence Length PDF.
-
english_sentence_length_variance.m
evaluates the variance of the English Sentence Length PDF.
-
english_word_length_cdf.m
evaluates the English Word Length CDF.
-
english_word_length_cdf_inv.m
inverts the English Word Length CDF.
-
english_word_length_mean.m
evaluates the mean of the English Word Length PDF.
-
english_word_length_pdf.m
evaluates the English Word Length PDF.
-
english_word_length_sample.m
samples the English Word Length PDF.
-
english_word_length_variance.m
evaluates the variance of the English Word Length PDF.
-
erlang_cdf.m
evaluates the Erlang CDF.
-
erlang_cdf_inv.m
inverts the Erlang CDF.
-
erlang_check.m
checks the parameters of the Erlang PDF.
-
erlang_mean.m
returns the mean of the Erlang PDF.
-
erlang_pdf.m
evaluates the Erlang PDF.
-
erlang_sample.m
samples the Erlang PDF.
-
erlang_variance.m
returns the variance of the Erlang PDF.
-
euler_constant.m
returns the value of the Euler-Mascheroni constant.
-
exponential_01_cdf.m
evaluates the Exponential 01 CDF.
-
exponential_01_cdf_inv.m
inverts the Exponential 01 CDF.
-
exponential_01_mean.m
returns the mean of the Exponential 01 PDF.
-
exponential_01_pdf.m
evaluates the Exponential 01 PDF.
-
exponential_01_sample.m
samples the Exponential PDF with parameter 1.
-
exponential_01_variance.m
returns the variance of the Exponential 01 PDF.
-
exponential_cdf.m
evaluates the Exponential CDF.
-
exponential_cdf_inv.m
inverts the Exponential CDF.
-
exponential_cdf_values.m
returns some values of the Exponential CDF.
-
exponential_check.m
checks the parameters of the Exponential CDF.
-
exponential_mean.m
returns the mean of the Exponential PDF.
-
exponential_pdf.m
evaluates the Exponential PDF.
-
exponential_sample.m
samples the Exponential PDF.
-
exponential_variance.m
returns the variance of the Exponential PDF.
-
extreme_values_cdf.m
evaluates the Extreme Values CDF.
-
extreme_values_cdf_inv.m
inverts the Extreme Values CDF.
-
extreme_values_cdf_values.m
returns some values of the Extreme Values CDF.
-
extreme_values_check.m
checks the parameters of the Extreme Values CDF.
-
extreme_values_mean.m
returns the mean of the Extreme Values PDF.
-
extreme_values_pdf.m
evaluates the Extreme Values PDF.
-
extreme_values_sample.m
samples the Extreme Values PDF.
-
extreme_values_variance.m
returns the variance of the Extreme Values PDF.
-
f_cdf.m
evaluates the F central CDF.
-
f_cdf_values.m
returns some values of the F central CDF test function.
-
f_check.m
checks the parameters of the F central PDF.
-
f_mean.m
returns the mean of the F central PDF.
-
f_pdf.m
evaluates the F central PDF.
-
f_sample.m
samples the F central PDF.
-
f_variance.m
returns the variance of the F central PDF.
-
f_noncentral_cdf_values.m
returns some values of the Noncentral F CDF.
-
f_noncentral_check.m
checks the parameters of the F noncentral PDF.
-
f_noncentral_mean.m
returns the mean of the F noncentral PDF.
-
f_noncentral_variance.m
returns the variance of the F noncentral PDF.
-
fermi_dirac_sample.m
samples the Fermi-Dirac distribution.
-
fisher_pdf.m
evaluates the Fisher PDF.
-
fisher_sample.m
samples the Fisher PDF.
-
fisk_cdf.m
evaluates the Fisk CDF.
-
fisk_cdf_inv.m
inverts the Fisk CDF.
-
fisk_check.m
checks the parameters of the Fisk PDF.
-
fisk_mean.m
returns the mean of the Fisk PDF.
-
fisk_pdf.m
evaluates the Fisk PDF.
-
fisk_sample.m
samples the Fisk PDF.
-
fisk_variance.m
returns the variance of the Fisk PDF.
-
folded_normal_cdf.m
evaluates the Folded Normal CDF.
-
folded_normal_cdf_inv.m
inverts the Folded Normal CDF.
-
folded_normal_check.m
checks the parameters of the Folded Normal CDF.
-
folded_normal_mean.m
returns the mean of the Folded Normal PDF.
-
folded_normal_pdf.m
evaluates the Folded Normal PDF.
-
folded_normal_sample.m
samples the Folded Normal PDF.
-
folded_normal_variance.m
returns the variance of the Folded Normal PDF.
-
frechet_cdf.m
evaluates the Frechet CDF.
-
frechet_cdf_inv.m
inverts the Frechet CDF.
-
frechet_mean.m
returns the mean of the Frechet PDF.
-
frechet_pdf.m
evaluates the Frechet PDF.
-
frechetk_sample.m
samples the Frechet PDF.
-
frechet_variance.m
returns the variance of the Frechet PDF.
-
gamma_cdf.m
evaluates the Gamma CDF.
-
gamma_cdf_values.m
returns some values of the Gamma CDF.
-
gamma_check.m
checks the parameters of the Gamma PDF.
-
gamma_inc_values.m
returns some values of the incomplete Gamma function.
-
gamma_mean.m
returns the mean of the Gamma PDF.
-
gamma_pdf.m
evaluates the Gamma PDF.
-
gamma_sample.m
samples the Gamma PDF.
-
gamma_variance.m
returns the variance of the Gamma PDF.
-
genlogistic_cdf.m
evaluates the Generalized Logistic CDF.
-
genlogistic_cdf_inv.m
inverts the Generalized Logistic CDF.
-
genlogistic_check.m
checks the parameters of the Generalized Logistic CDF.
-
genlogistic_mean.m
returns the mean of the Generalized Logistic PDF.
-
genlogistic_pdf.m
evaluates the Generalized Logistic PDF.
-
genlogistic_sample.m
samples the Generalized Logistic PDF.
-
genlogistic_variance.m
returns the variance of the Generalized Logistic PDF.
-
geometric_cdf.m
evaluates the Geometric CDF.
-
geometric_cdf_inv.m
inverts the Geometric CDF.
-
geometric_cdf_values.m
returns some values of the Geometric CDF.
-
geometric_check.m
checks the parameter of the Geometric CDF.
-
geometric_mean.m
returns the mean of the Geometric PDF.
-
geometric_pdf.m
evaluates the Geometric PDF.
-
geometric_sample.m
samples the Geometric PDF.
-
geometric_variance.m
returns the variance of the Geometric PDF.
-
gompertz_cdf.m
evaluates the Gompertz CDF.
-
gompertz_cdf_inv.m
inverts the Gompertz CDF.
-
gompertz_check.m
checks the parameters of the Gompertz PDF.
-
gompertz_pdf.m
evaluates the Gompertz PDF.
-
gompertz_sample.m
samples the Gompertz PDF.
-
gumbel_cdf.m
evaluates the Gumbel CDF.
-
gumbel_cdf_inv.m
inverts the Gumbel CDF.
-
gumbel_mean.m
returns the mean of the Gumbel PDF.
-
gumbel_pdf.m
evaluates the Gumbel PDF.
-
gumbel_sample.m
samples the Gumbel PDF.
-
gumbel_variance.m
returns the variance of the Gumbel PDF.
-
half_normal_cdf.m
evaluates the Half Normal CDF.
-
half_normal_cdf_inv.m
inverts the Half Normal CDF.
-
half_normal_check.m
checks the parameters of the Half Normal PDF.
-
half_normal_mean.m
returns the mean of the Half Normal PDF.
-
half_normal_pdf.m
evaluates the Half Normal PDF.
-
half_normal_sample.m
samples the Half Normal PDF.
-
half_normal_variance.m
returns the variance of the Half Normal PDF.
-
hypergeometric_cdf.m
evaluates the Hypergeometric CDF.
-
hypergeometric_cdf_values.m
returns some values of the Hypergeometric CDF.
-
hypergeometric_check.m
checks the parameters of the Hypergeometric CDF.
-
hypergeometric_mean.m
returns the mean of the Hypergeometric PDF.
-
hypergeometric_pdf.m
evaluates the Hypergeometric PDF.
-
hypergeometric_sample.m
samples the Hypergeometric PDF.
-
hypergeometric_variance.m
returns the variance of the Hypergeometric PDF.
-
i4_choose_log.m,
computes the logarithm of the binomial coefficient C(N,K);
-
i4_is_power_of_10.m,
returns TRUE if an I4 is a power of 10;
-
i4_mop.m,
returns a power of -1;
-
i4_uniform_ab.m,
returns a pseudorandom I4 between A and B;
-
i4row_max.m
returns the maximums of rows of an I4ROW.
-
i4row_mean.m
returns the means of the rows of an I4ROW.
-
i4row_min.m
returns the minimums of rows of an I4ROW.
-
i4row_variance.m
returns the variances of the rows of an I4ROW.
-
i4vec_print.m
prints an I4VEC.
-
i4vec_run_count.m
counts the runs of equal values in an I4VEC.
-
i4vec_uniform_ab.m,
returns a pseudorandom I4VEC in a given range;
-
i4vec_unique_count.m,
counts the number of unique elements in an unsorted I4VEC;
-
inverse_gaussian_cdf.m
evaluates the Inverse Gaussian CDF.
-
inverse_gaussian_check.m
checks the parameters of the Inverse Gaussian CDF.
-
inverse_gaussian_mean.m
returns the mean of the Inverse Gaussian PDF.
-
inverse_gaussian_pdf.m
evaluates the Inverse Gaussian PDF.
-
inverse_gaussian_sample.m
samples the Inverse Gaussian PDF.
-
inverse_gaussian_variance.m
returns the variance of the Inverse Gaussian PDF.
-
laplace_cdf.m
evaluates the Laplace CDF.
-
laplace_cdf_inv.m
inverts the Laplace CDF.
-
laplace_cdf_values.m
returns some values of the Laplace CDF.
-
laplace_check.m
checks the parameters of the Laplace PDF.
-
laplace_mean.m
returns the mean of the Laplace PDF.
-
laplace_pdf.m
evaluates the Laplace PDF.
-
laplace_sample.m
samples the Laplace PDF.
-
laplace_variance.m
returns the variance of the Laplace PDF.
-
lerch.m
estimates the Lerch transcendent function.
-
levy_cdf.m
evaluates the Levy CDF.
-
levy_cdf_inv.m
inverts the Levy CDF.
-
levy_pdf.m
evaluates the Levy PDF.
-
levy_sample.m
samples the Levy PDF.
-
logistic_cdf.m
evaluates the Logistic CDF.
-
logistic_cdf_inv.m
inverts the Logistic CDF.
-
logistic_cdf_values.m
returns some values of the Logistic CDF.
-
logistic_check.m
checks the parameters of the Logistic CDF.
-
logistic_mean.m
returns the mean of the Logistic PDF.
-
logistic_pdf.m
evaluates the Logistic PDF.
-
logistic_sample.m
samples the Logistic PDF.
-
logistic_variance.m
returns the variance of the Logistic PDF.
-
log_normal_cdf.m
evaluates the Lognormal CDF.
-
log_normal_cdf_inv.m
inverts the Lognormal CDF.
-
log_normal_cdf_values.m
returns some values of the Log Normal CDF.
-
log_normal_check.m
checks the parameters of the Lognormal PDF.
-
log_normal_mean.m
returns the mean of the Lognormal PDF.
-
log_normal_pdf.m
evaluates the Lognormal PDF.
-
log_normal_sample.m
samples the Lognormal PDF.
-
log_normal_variance.m
returns the variance of the Lognormal PDF.
-
log_series_cdf.m
evaluates the Logarithmic Series CDF.
-
log_series_cdf_inv.m
inverts the Logarithmic Series CDF.
-
log_series_cdf_values.m
returns some values of the Log Series CDF.
-
log_series_check.m
checks the parameter of the Logarithmic Series PDF.
-
log_series_mean.m
returns the mean of the Logarithmic Series PDF.
-
log_series_pdf.m
evaluates the Logarithmic Series PDF.
-
log_series_sample.m
samples the Logarithmic Series PDF.
-
log_series_variance.m
returns the variance of the Logarithmic Series PDF.
-
log_uniform_cdf.m
evaluates the Log Uniform CDF.
-
log_uniform_cdf_inv.m
inverts the Log Uniform CDF.
-
log_uniform_check.m
checks the parameters of the Log Uniform PDF.
-
log_uniform_mean.m
returns the mean of the Log Uniform PDF.
-
log_uniform_pdf.m
evaluates the Log Uniform PDF.
-
log_uniform_sample.m
samples the Log Uniform PDF.
-
log_uniform_variance.m
returns the variance of the Log Uniform PDF.
-
lorentz_cdf.m
evaluates the Lorentz CDF.
-
lorentz_cdf_inv.m
inverts the Lorentz CDF.
-
lorentz_mean.m
returns the mean of the Lorentz PDF.
-
lorentz_pdf.m
evaluates the Lorentz PDF.
-
lorentz_sample.m
samples the Lorentz PDF.
-
lorentz_variance.m
returns the variance of the Lorentz PDF.
-
maxwell_cdf.m
evaluates the Maxwell CDF.
-
maxwell_cdf_inv.m
inverts the Maxwell CDF.
-
maxwell_check.m
checks the parameters of the Maxwell CDF.
-
maxwell_mean.m
returns the mean of the Maxwell PDF.
-
maxwell_pdf.m
evaluates the Maxwell PDF.
-
maxwell_sample.m
samples the Maxwell PDF.
-
maxwell_variance.m
returns the variance of the Maxwell PDF.
-
multicoef_check.m
checks the parameters of the multinomial coefficient.
-
multinomial_coef1.m
computes a Multinomial coefficient.
-
multinomial_coef2.m
computes a Multinomial coefficient.
-
multinomial_check.m
checks the parameters of the Multinomial PDF.
-
multinomial_covariance.m
returns the covariances of the Multinomial PDF.
-
multinomial_mean.m
returns the means of the Multinomial PDF.
-
multinomial_pdf.m
computes a Multinomial PDF.
-
multinomial_sample.m
samples the Multinomial PDF.
-
multinomial_variance.m
returns the variances of the Multinomial PDF.
-
multinoulli_pdf.m
evaluates the Multinoulli PDF.
-
multivariate_normal_sample.m
samples the Multivariate Normal PDF.
-
nakagami_cdf.m
evaluates the Nakagami CDF.
-
nakagami_cdf_inv.m
inverts the Nakagami CDF.
-
nakagami_check.m
checks the parameters of the Nakagami PDF.
-
nakagami_mean.m
returns the mean of the Nakagami PDF.
-
nakagami_pdf.m
evaluates the Nakagami PDF.
-
nakagami_variance.m
returns the variance of the Nakagami PDF.
-
negative_binomial_cdf.m
evaluates the Negative Binomial CDF.
-
negative_binomial_cdf_inv.m
inverts the Negative Binomial CDF.
-
negative_binomial_cdf_values.m
returns some values of the Negative Binomial CDF.
-
negative_binomial_check.m
checks the parameters of the Negative Binomial PDF.
-
negative_binomial_mean.m
returns the mean of the Negative Binomial PDF.
-
negative_binomial_pdf.m
evaluates the Negative Binomial PDF.
-
negative_binomial_sample.m
samples the Negative Binomial PDF.
-
negative_binomial_variance.m
returns the variance of the Negative Binomial PDF.
-
normal_01_cdf.m
evaluates the Normal 01 CDF.
-
normal_01_cdf_inv.m
inverts the Normal 01 CDF.
-
normal_01_cdf_values.m
returns some values of the Normal 01 CDF.
-
normal_01_mean.m
returns the mean of the Normal 01 PDF.
-
normal_01_pdf.m
evaluates the Normal 01 PDF.
-
normal_01_sample.m
a sample of the standard normal probability distribution.
-
normal_01_samples.m
multiple samples of the standard normal probability distribution.
-
normal_01_variance.m
returns the variance of the Normal 01 PDF.
-
normal_01_vector.m
samples the standard normal probability distribution.
-
normal_cdf.m
evaluates the Normal CDF.
-
normal_cdf_inv.m
inverts the Normal CDF.
-
normal_cdf_values.m
returns some values of the Normal CDF.
-
normal_check.m
checks the parameters of the Normal PDF.
-
normal_mean.m
returns the mean of the Normal PDF.
-
normal_pdf.m
evaluates the Normal PDF.
-
normal_sample.m
a sample of the Normal PDF.
-
normal_samples.m
multiple samples of the Normal PDF.
-
normal_variance.m
returns the variance of the Normal PDF.
-
normal_truncated_ab_cdf.m
evaluates the Truncated Normal CDF.
-
normal_truncated_ab_cdf_inv.m
inverts the Truncated Normal CDF.
-
normal_truncated_ab_mean.m
returns the mean of the Truncated Normal PDF.
-
normal_truncated_ab_pdf.m
evaluates the Truncated Normal PDF.
-
normal_truncated_ab_sample.m
samples the Truncated Normal PDF.
-
normal_truncated_ab_variance.m
returns the variance of the Truncated Normal PDF.
-
normal_truncated_a_cdf.m
evaluates the lower Truncated Normal CDF.
-
normal_truncated_a_cdf_inv.m
inverts the lower Truncated Normal CDF.
-
normal_truncated_a_mean.m
returns the mean of the lower Truncated Normal PDF.
-
normal_truncated_a_pdf.m
evaluates the lower Truncated Normal PDF.
-
normal_truncated_a_sample.m
samples the lower Truncated Normal PDF.
-
normal_truncated_a_variance.m
returns the variance of the lower Truncated Normal PDF.
-
normal_truncated_b_cdf.m
evaluates the upper Truncated Normal CDF.
-
normal_truncated_b_cdf_inv.m
inverts the upper Truncated Normal CDF.
-
normal_truncated_b_mean.m
returns the mean of the upper Truncated Normal PDF.
-
normal_truncated_b_pdf.m
evaluates the upper Truncated Normal PDF.
-
normal_truncated_b_sample.m
samples the upper Truncated Normal PDF.
-
normal_truncated_b_variance.m
returns the variance of the upper Truncated Normal PDF.
-
normal_vector.m
samples the normal probability distribution.
-
owen_values.m
returns values of Owen's T function.
-
pareto_cdf.m
evaluates the Pareto CDF.
-
pareto_cdf_inv.m
inverts the Pareto CDF.
-
pareto_check.m
checks the parameters of the Pareto CDF.
-
pareto_mean.m
returns the mean of the Pareto PDF.
-
pareto_pdf.m
evaluates the Pareto PDF.
-
pareto_sample.m
samples the Pareto PDF.
-
pareto_variance.m
returns the variance of the Pareto PDF.
-
pearson_05_check.m
checks the parameters of the Pearson 05 PDF.
-
pearson_05_mean.m
evaluates the mean of the Pearson 05 PDF.
-
pearson_05_pdf.m
evaluates the Pearson 05 PDF.
-
pearson_05_sample.m
samples the Pearson 05 PDF.
-
planck_check.m
checks the parameters of the Planck PDF.
-
planck_mean.m
returns the mean of the Planck PDF.
-
planck_pdf.m
evaluates the Planck PDF.
-
planck_sample.m
samples the Planck PDF.
-
planck_variance.m
returns the variance of the Planck PDF.
-
point_distance_1d_pdf.m
evaluates the point distance PDF in 1D.
-
point_distance_2d_pdf.m
evaluates the point distance PDF in 2D.
-
point_distance_3d_pdf.m
evaluates the point distance PDF in the 3D.
-
poisson_cdf.m
evaluates the Poisson CDF.
-
poisson_cdf_inv.m
inverts the Poisson CDF.
-
poisson_cdf_values.m
returns some values of the Poisson CDF.
-
poisson_check.m
checks the parameter of the Poisson PDF.
-
poisson_kernel.m
evaluates the Poisson kernel.
-
poisson_mean.m
returns the mean of the Poisson PDF.
-
poisson_pdf.m
evaluates the Poisson PDF.
-
poisson_sample.m
samples the Poisson PDF.
-
poisson_variance.m
returns the variance of the Poisson PDF.
-
power_cdf.m
evaluates the Power CDF.
-
power_cdf_inv.m
inverts the Power CDF.
-
power_check.m
checks the parameter of the Power PDF.
-
power_mean.m
returns the mean of the Power PDF.
-
power_pdf.m
evaluates the Power PDF.
-
power_sample.m
samples the Power PDF.
-
power_variance.m
returns the variance of the Power PDF.
-
psi_values.m
returns some values of the Psi or Digamma function.
-
quasigeometric_cdf.m
evaluates the Quasigeometric CDF.
-
quasigeometric_cdf_inv.m
inverts the Quasigeometric CDF.
-
quasigeometric_check.m
checks the parameters of the Quasigeometric CDF.
-
quasigeometric_mean.m
returns the mean of the Quasigeometric PDF.
-
quasigeometric_pdf.m
evaluates the Quasigeometric PDF.
-
quasigeometric_sample.m
samples the Quasigeometric PDF.
-
quasigeometric_variance.m
returns the variance of the Quasigeometric PDF.
-
r8_beta.m
returns the value of the Beta function.
-
r8_gamma_inc.m
computes the incomplete Gamma function.
-
r8_gamma_log_int.m
computes the logarithm of Gamma of an integer N.
-
r8_uniform_01.m
is a portable pseudorandom number generator.
-
r8_zeta.m
estimates the Riemann Zeta function.
-
r8mat_print.m,
prints an R8MAT;
-
r8mat_print_some.m,
prints some of an R8MAT;
-
r8mat_uniform_01.m
returns an R8MAT. of random double precision values in [0,1].
-
r8poly_value_horner.m
evaluates a polynomial.
-
r8row_max.m
returns the maximums of rows of an R8ROW.
-
r8row_mean.m
returns the means of rows of an R8ROW.
-
r8row_min.m
returns the minimums of rows of an R8ROW.
-
r8row_variance.m
returns the variances of the rows of an R8ROW.
-
r8vec_circular_variance.m
returns the circular variance in an R8VEC.
-
r8vec_diff_norm.m,
returns the L2 norm of the difference of two R8VEC's.
-
r8vec_max.m
returns the maximum value in an R8VEC.
-
r8vec_mean.m
returns the mean of an R8VEC.
-
r8vec_min.m
returns the minimum value in an R8VEC.
-
r8vec_print.m
prints an R8VEC.
-
r8vec_uniform_01.m
returns an R8VEC. of random double precision values in [0,1].
-
r8vec_unit_sum.m
normalizes an R8VEC. to have unit sum.
-
r8vec_variance.m
returns the variance of an R8VEC..
-
rayleigh_cdf.m
evaluates the Rayleigh CDF.
-
rayleigh_cdf_inv.m
inverts the Rayleigh CDF.
-
rayleigh_cdf_values.m
returns some values of the Rayleigh CDF.
-
rayleigh_check.m
checks the parameter of the Rayleigh PDF.
-
rayleigh_mean.m
returns the mean of the Rayleigh PDF.
-
rayleigh_pdf.m
evaluates the Rayleigh PDF.
-
rayleigh_sample.m
samples the Rayleigh PDF.
-
rayleigh_variance.m
returns the variance of the Rayleigh PDF.
-
reciprocal_cdf.m
evaluates the Reciprocal CDF.
-
reciprocal_cdf_inv.m
inverts the Reciprocal CDF.
-
reciprocal_check.m
checks the parameters of the Reciprocal CDF.
-
reciprocal_mean.m
returns the mean of the Reciprocal PDF.
-
reciprocal_pdf.m
evaluates the Reciprocal PDF.
-
reciprocal_sample.m
samples the Reciprocal PDF.
-
reciprocal_variance.m
returns the variance of the Reciprocal PDF.
-
ribesl.m
evaluates an I Bessel function of NONINTEGER order.
-
runs_mean.m
returns the mean of the Runs PDF.
-
runs_pdf.m
evaluates the Runs PDF.
-
runs_sample.m
samples the Runs PDF.
-
runs_simulate.m
simulates the Runs PDF.
-
runs_variance.m
returns the variance of the Runs PDF.
-
sech_cdf.m
evaluates the Hyperbolic Secant CDF.
-
sech_cdf_inv.m
inverts the Hyperbolic Secant CDF.
-
sech_check.m
checks the parameters of the Hyperbolic Secant CDF.
-
sech_mean.m
returns the mean of the Hyperbolic Secant PDF.
-
sech_pdf.m
evaluates the Hypebolic Secant PDF.
-
sech_sample.m
samples the Hyperbolic Secant PDF.
-
sech_variance.m
returns the variance of the Hyperbolic Secant PDF.
-
semicircular_cdf.m
evaluates the Semicircular CDF.
-
semicircular_cdf_inv.m
inverts the Semicircular CDF.
-
semicircular_check.m
checks the parameters of the Semicircular CDF.
-
semicircular_mean.m
returns the mean of the Semicircular PDF.
-
semicircular_pdf.m
evaluates the Semicircular PDF.
-
semicircular_sample.m
samples the Semicircular PDF.
-
semicircular_variance.m
returns the variance of the Semicircular PDF.
-
sin_power_int.m
returns the integral of the N-th power of the sine function.
-
sphere_unit_area_nd.m,
returns the area of a unit sphere in ND;
-
stirling2_number.m
returns a value of the Stirling numbers of the second kind.
-
student_cdf.m
evaluates the central Student T CDF.
-
student_cdf_values.m
returns some values of the Student CDF.
-
student_check.m
checks the parameter of the central Student T CDF.
-
student_mean.m
returns the mean of the central Student T PDF.
-
student_pdf.m
evaluates the central Student T PDF.
-
student_sample.m
samples the central Student T PDF.
-
student_variance.m
returns the variance of the central Student T PDF.
-
student_noncentral_cdf.m
evaluates the noncentral Student T CDF.
-
student_noncentral_cdf_values.m
returns some values of the Noncentral Student CDF.
-
tfn.m
calculates the T function of Owen.
-
triangle_cdf.m
evaluates the Triangle CDF.
-
triangle_cdf_inv.m
inverts the Triangle CDF.
-
triangle_check.m
checks the parameters of the Triangle CDF.
-
triangle_mean.m
returns the mean of the Triangle PDF.
-
triangle_pdf.m
evaluates the Triangle PDF.
-
triangle_sample.m
samples the Triangle PDF.
-
triangle_variance.m
returns the variance of the Triangle PDF.
-
triangular_cdf.m
evaluates the Triangular CDF.
-
triangular_cdf_inv.m
inverts the Triangular CDF.
-
triangular_check.m
checks the parameters of the Triangular CDF.
-
triangular_mean.m
returns the mean of the Triangular PDF.
-
triangular_pdf.m
evaluates the Triangular PDF.
-
triangular_sample.m
samples the Triangular PDF.
-
triangular_variance.m
returns the variance of the Triangular PDF.
-
trigamma.m
calculates trigamma(x) = d^2 log(Gamma(x)) / dx^2.
-
trigamma_values.m
selected values of the Trigamma function.
-
uniform_01_cdf.m
evaluates the Uniform 01 CDF.
-
uniform_01_cdf_inv.m
inverts the Uniform 01 CDF.
-
uniform_01_mean.m
returns the mean of the Uniform 01 PDF.
-
uniform_01_order_sample.m
samples the Uniform 01 Order PDF.
-
uniform_01_pdf.m
evaluates the Uniform 01 PDF.
-
uniform_01_sample.m
samples the Uniform 01 PDF.
-
uniform_01_variance.m
returns the variance of the Uniform 01 PDF.
-
uniform_cdf.m
evaluates the Uniform CDF.
-
uniform_cdf_inv.m
inverts the Uniform CDF.
-
uniform_check.m
checks the parameters of the Uniform CDF.
-
uniform_mean.m
returns the mean of the Uniform PDF.
-
uniform_pdf.m
evaluates the Uniform PDF.
-
uniform_sample.m
samples the Uniform PDF.
-
uniform_variance.m
returns the variance of the Uniform PDF.
-
uniform_discrete_cdf.m
evaluates the Uniform Discrete CDF.
-
uniform_discrete_cdf_inv.m
inverts the Uniform Discrete CDF.
-
uniform_discrete_check.m
checks the parameters of the Uniform discrete CDF.
-
uniform_discrete_mean.m
returns the mean of the Uniform discrete PDF.
-
uniform_discrete_pdf.m
evaluates the Uniform discrete PDF.
-
uniform_discrete_sample.m
samples the Uniform discrete PDF.
-
uniform_discrete_variance.m
returns the variance of the Uniform discrete PDF.
-
uniform_nsphere_sample.m
samples the Uniform Unit Sphere PDF.
-
von_mises_cdf.m
evaluates the von Mises CDF.
-
von_mises_cdf_inv.m
inverts the von Mises CDF.
-
von_mises_cdf_values.m
returns some values of the von Mises CDF.
-
von_mises_check.m
checks the parameters of the von Mises PDF.
-
von_mises_circular_variance.m
returns the circular variance of the von Mises PDF.
-
von_mises_mean.m
returns the mean of the von Mises PDF.
-
von_mises_pdf.m
evaluates the von Mises PDF.
-
von_mises_sample.m
samples the von Mises PDF.
-
weibull_cdf.m
evaluates the Weibull CDF.
-
weibull_cdf_inv.m
inverts the Weibull CDF.
-
weibull_cdf_values.m
returns some values of the Weibull CDF.
-
weibull_check.m
checks the parameters of the Weibull CDF.
-
weibull_mean.m
returns the mean of the Weibull PDF.
-
weibull_pdf.m
evaluates the Weibull PDF.
-
weibull_sample.m
samples the Weibull PDF.
-
weibull_variance.m
returns the variance of the Weibull PDF.
-
weibull_discrete_cdf.m
evaluates the Discrete Weibull CDF.
-
weibull_discrete_cdf_inv.m
inverts the Discrete Weibull CDF.
-
weibull_discrete_check.m
checks the parameters of the discrete Weibull CDF.
-
weibull_discrete_pdf.m
evaluates the discrete Weibull PDF.
-
weibull_discrete_sample.m
samples the discrete Weibull PDF.
-
zipf_cdf.m
evaluates the Zipf CDF.
-
zipf_check.m
checks the parameter of the Zipf PDF.
-
zipf_mean.m
returns the mean of the Zipf PDF.
-
zipf_pdf.m
evaluates the Zipf PDF.
-
zipf_sample.m
samples the Zipf PDF.
-
zipf_variance.m
returns the variance of the Zipf PDF.
Last revised on 01 November 2024.