05 May 2021 08:15:27 AM cdflib_test(): C version Test cdflib(). beta_test BETA evaluates the Beta function; GAMMA_X evaluates the Gamma function. Argument A = 2.2 Argument B = 3.7 Beta(A,B) = 0.045376 (Expected value = 0.0454 ) Gamma(A)*Gamma(B)/Gamma(A+B) = 0.045376 beta_inc_test BETA_INC computes the incomplete Beta ratio. BETA_INC_CDF_VALUES looks up some values. X Y A B CDF CDF (Lookup) (Computed) 0.01 0.99 0.5 0.5 0.0637686 0.0637686 0.1 0.9 0.5 0.5 0.204833 0.204833 1 0 0.5 0.5 1 1 0 1 1 0.5 0 0 0.01 0.99 1 0.5 0.0050126 0.00501256 0.1 0.9 1 0.5 0.0513167 0.0513167 0.5 0.5 1 0.5 0.292893 0.292893 0.5 0.5 1 1 0.5 0.5 0.1 0.9 2 2 0.028 0.028 0.2 0.8 2 2 0.104 0.104 0.3 0.7 2 2 0.216 0.216 0.4 0.6 2 2 0.352 0.352 0.5 0.5 2 2 0.5 0.5 0.6 0.4 2 2 0.648 0.648 0.7 0.3 2 2 0.784 0.784 0.8 0.2 2 2 0.896 0.896 0.9 0.1 2 2 0.972 0.972 0.5 0.5 5.5 5 0.436191 0.436191 0.9 0.1 10 0.5 0.151641 0.151641 0.5 0.5 10 5 0.0897827 0.0897827 1 0 10 5 1 1 0.5 0.5 10 10 0.5 0.5 0.8 0.2 20 5 0.459877 0.459877 0.6 0.4 20 10 0.214682 0.214682 0.8 0.2 20 10 0.950736 0.950736 0.5 0.5 20 20 0.5 0.5 0.6 0.4 20 20 0.897941 0.897941 0.7 0.3 30 10 0.22413 0.22413 0.8 0.2 30 10 0.758641 0.758641 0.7 0.3 40 20 0.700178 0.700178 X Y A B 1-CDF CCDF (Lookup) (Computed) 0.01 0.99 0.5 0.5 0.936231 0.936231 0.1 0.9 0.5 0.5 0.795167 0.795167 1 0 0.5 0.5 0 0 0 1 1 0.5 1 1 0.01 0.99 1 0.5 0.994987 0.994987 0.1 0.9 1 0.5 0.948683 0.948683 0.5 0.5 1 0.5 0.707107 0.707107 0.5 0.5 1 1 0.5 0.5 0.1 0.9 2 2 0.972 0.972 0.2 0.8 2 2 0.896 0.896 0.3 0.7 2 2 0.784 0.784 0.4 0.6 2 2 0.648 0.648 0.5 0.5 2 2 0.5 0.5 0.6 0.4 2 2 0.352 0.352 0.7 0.3 2 2 0.216 0.216 0.8 0.2 2 2 0.104 0.104 0.9 0.1 2 2 0.028 0.028 0.5 0.5 5.5 5 0.563809 0.563809 0.9 0.1 10 0.5 0.848359 0.848359 0.5 0.5 10 5 0.910217 0.910217 1 0 10 5 0 0 0.5 0.5 10 10 0.5 0.5 0.8 0.2 20 5 0.540123 0.540123 0.6 0.4 20 10 0.785318 0.785318 0.8 0.2 20 10 0.0492635 0.0492635 0.5 0.5 20 20 0.5 0.5 0.6 0.4 20 20 0.102059 0.102059 0.7 0.3 30 10 0.77587 0.77587 0.8 0.2 30 10 0.241359 0.241359 0.7 0.3 40 20 0.299822 0.299822 cdfbet_test CDFBET computes one missing parameter from the BETA CDF: BETA_CDF ( (P,Q), (X,Y), A, B ) P Q X Y A B 0.261719 0.738281 0.25 0.75 2 3 0.261719 0.738281 0.25 0.75 2 3 0.261719 0.738281 0.25 0.75 2 3 0.261719 0.738281 0.25 0.75 2 3 cdfbin_test CDFBIN computes one missing parameter from the Binomial CDF: BINOMIAL_CDF ( (P,Q), S, XN, (PR,OMPR) ) P Q S XN PR OMPR 0.0673472 0.932653 5 8 0.875 0.125 0.067347 0.932653 5 8 0.875 0.125 0.067347 0.932653 5 8 0.875 0.125 0.067347 0.932653 5 8 0.875 0.125 cdfchi_test CDFCHI computes one missing parameter from the Chi Square CDF: CHI_CDF ( (P,Q), X, DF ) P Q X DF 0.242424 0.757576 5 8 0.242424 0.757576 5 8 0.242424 0.757576 5 8 cdfchn_test CDFCHN computes one missing parameter from the Chi Square CDF: CHI_Noncentral_CDF ( (P,Q), X, DF, PNONC ) P Q X DF PNONC 0.21104 0.78896 5 8 0.5 0.21104 0.78896 5 8 0.5 0.21104 0.78896 5 7.99999 0.5 0.21104 0.78896 5 8 0.499992 cdff_test CDFF computes one missing parameter from the F CDF: F_CDF ( (P,Q), F, DFN, DFD ) P Q F DFN DFD 0.89351 0.10649 5 8 3 0.89351 0.10649 5 8 3 0.89351 0.10649 5 8.00034 3 0.89351 0.10649 5 8 3 cdffnc_test CDFFNC computes one missing parameter from the noncentral F CDF: F_noncentral_CDF ( (P,Q), F, DFN, DFD, PNONC ) P Q F DFN DFD PNONC 0.6 0.4 5 8 3 17.648 0.6 0.4 5 8 3 17.648 0.6 0.4 5 8 3 17.648 0.6 0.4 5 8 3 17.648 0.6 0.4 5 8 3 17.648 cdfgam_test CDFGAM computes one missing parameter from the Gamma CDF: Gamma_CDF ( (P,Q), X, SHAPE, SCALE ) P Q X SHAPE SCALE 0.981998 0.0180022 5 8 3 0.981998 0.018002 5.00001 8 3 0.981998 0.018002 5 7.99999 3 0.981998 0.018002 5 8 3 cdfnbn_test CDFNBN computes one missing parameter from the negative Binomial CDF: negative binomial CDF ( (P,Q), F, S, (PR,OMPR) ) P Q F S PR OMPR 0.988752 0.0112478 3 5 0.875 0.125 0.988752 0.011248 2.99999 5 0.875 0.125 0.988752 0.011248 3 5.00003 0.875 0.125 0.988752 0.011248 3 5 0.874999 0.125001 cdfnor_test CDFNOR computes one missing parameter from the Normal CDF: Normal_CDF ( (P,Q), X, MEAN, SD ) P Q X MEAN SD 0.0111355 0.988865 3 5 0.875 0.011135 0.988865 2.99999 5 0.875 0.011135 0.988865 3 5.00001 0.875 0.011135 0.988865 3 5 0.874994 cdfpoi_test CDFPOI computes one missing parameter from the Poisson CDF: POISSON_CDF ( (P,Q), S, XLAM ) P Q S XLAM 0.265026 0.734974 3 5 0.265026 0.734974 3 5 0.265026 0.734974 3 5 cdft_test CDFT computes one missing parameter from the T CDF: T_CDF ( (P,Q), T, DF ) P Q T DF 0.98495 0.0150496 3 5 0.98495 0.01505 2.99998 5 CDFT returned STATUS = 2 cumbet_test CUMBET computes the Beta CDF and the complementary CDF. BETA_INC_CDF_VALUES looks up some values. X Y A B CDF CDF (Lookup) (Computed) 0.01 0.99 0.5 0.5 0.0637686 0.0637686 0.1 0.9 0.5 0.5 0.204833 0.204833 1 0 0.5 0.5 1 1 0 1 1 0.5 0 0 0.01 0.99 1 0.5 0.0050126 0.00501256 0.1 0.9 1 0.5 0.0513167 0.0513167 0.5 0.5 1 0.5 0.292893 0.292893 0.5 0.5 1 1 0.5 0.5 0.1 0.9 2 2 0.028 0.028 0.2 0.8 2 2 0.104 0.104 0.3 0.7 2 2 0.216 0.216 0.4 0.6 2 2 0.352 0.352 0.5 0.5 2 2 0.5 0.5 0.6 0.4 2 2 0.648 0.648 0.7 0.3 2 2 0.784 0.784 0.8 0.2 2 2 0.896 0.896 0.9 0.1 2 2 0.972 0.972 0.5 0.5 5.5 5 0.436191 0.436191 0.9 0.1 10 0.5 0.151641 0.151641 0.5 0.5 10 5 0.0897827 0.0897827 1 0 10 5 1 1 0.5 0.5 10 10 0.5 0.5 0.8 0.2 20 5 0.459877 0.459877 0.6 0.4 20 10 0.214682 0.214682 0.8 0.2 20 10 0.950736 0.950736 0.5 0.5 20 20 0.5 0.5 0.6 0.4 20 20 0.897941 0.897941 0.7 0.3 30 10 0.22413 0.22413 0.8 0.2 30 10 0.758641 0.758641 0.7 0.3 40 20 0.700178 0.700178 X Y A B 1-CDF CCDF (Lookup) (Computed) 0.01 0.99 0.5 0.5 0.936231 0.936231 0.1 0.9 0.5 0.5 0.795167 0.795167 1 0 0.5 0.5 0 0 0 1 1 0.5 1 1 0.01 0.99 1 0.5 0.994987 0.994987 0.1 0.9 1 0.5 0.948683 0.948683 0.5 0.5 1 0.5 0.707107 0.707107 0.5 0.5 1 1 0.5 0.5 0.1 0.9 2 2 0.972 0.972 0.2 0.8 2 2 0.896 0.896 0.3 0.7 2 2 0.784 0.784 0.4 0.6 2 2 0.648 0.648 0.5 0.5 2 2 0.5 0.5 0.6 0.4 2 2 0.352 0.352 0.7 0.3 2 2 0.216 0.216 0.8 0.2 2 2 0.104 0.104 0.9 0.1 2 2 0.028 0.028 0.5 0.5 5.5 5 0.563809 0.563809 0.9 0.1 10 0.5 0.848359 0.848359 0.5 0.5 10 5 0.910217 0.910217 1 0 10 5 0 0 0.5 0.5 10 10 0.5 0.5 0.8 0.2 20 5 0.540123 0.540123 0.6 0.4 20 10 0.785318 0.785318 0.8 0.2 20 10 0.0492635 0.0492635 0.5 0.5 20 20 0.5 0.5 0.6 0.4 20 20 0.102059 0.102059 0.7 0.3 30 10 0.77587 0.77587 0.8 0.2 30 10 0.241359 0.241359 0.7 0.3 40 20 0.299822 0.299822 cumbin_test CUMBIN computes the Binomial CDF and the complementary CDF. BINOMIAL_CDF_VALUES looks up some values. X S Pr CDF CDF (Lookup) (Computed) 0 2 0.05 0.9025 0.9025 1 2 0.05 0.9975 0.9975 2 2 0.05 1 1 0 2 0.5 0.25 0.25 1 2 0.5 0.75 0.75 0 4 0.25 0.3164 0.316406 1 4 0.25 0.7383 0.738281 2 4 0.25 0.9492 0.949219 3 4 0.25 0.9961 0.996094 4 10 0.05 0.9999 0.999936 4 10 0.1 0.9984 0.998365 4 10 0.15 0.9901 0.990126 4 10 0.2 0.9672 0.967207 4 10 0.25 0.9219 0.921873 4 10 0.3 0.8497 0.849732 4 10 0.4 0.6331 0.633103 4 10 0.5 0.377 0.376953 X S Pr 1-CDF CCDF (Lookup) (Computed) 0 2 0.05 0.0975 0.0975 1 2 0.05 0.0025 0.0025 2 2 0.05 0 0 0 2 0.5 0.75 0.75 1 2 0.5 0.25 0.25 0 4 0.25 0.6836 0.683594 1 4 0.25 0.2617 0.261719 2 4 0.25 0.0508 0.0507813 3 4 0.25 0.0039 0.00390625 4 10 0.05 0.0001 6.36898e-05 4 10 0.1 0.0016 0.00163494 4 10 0.15 0.0099 0.00987409 4 10 0.2 0.0328 0.0327935 4 10 0.25 0.0781 0.0781269 4 10 0.3 0.1503 0.150268 4 10 0.4 0.3669 0.366897 4 10 0.5 0.623 0.623047 cumchi_test CUMCHI computes the chi square CDF and the complementary CDF. CHI_SQUARE_CDF_VALUES looks up some values. X DF CDF CDF (Lookup) (Computed) 0.01 1 0.0796557 0.0796557 0.01 2 0.00498752 0.00498752 0.02 1 0.112463 0.112463 0.02 2 0.00995017 0.00995017 0.4 1 0.472911 0.472911 0.4 2 0.181269 0.181269 0.4 3 0.0597575 0.0597575 0.4 4 0.0175231 0.0175231 1 1 0.682689 0.682689 1 2 0.393469 0.393469 1 3 0.198748 0.198748 1 4 0.090204 0.090204 1 5 0.0374342 0.0374342 2 3 0.427593 0.427593 3 3 0.608375 0.608375 4 3 0.738536 0.738536 5 3 0.828203 0.828203 6 3 0.88839 0.88839 1 10 0.000172116 0.000172116 2 10 0.00365985 0.00365985 3 10 0.0185759 0.0185759 X DF 1-CDF CCDF (Lookup) (Computed) 0.01 1 0.920344 0.920344 0.01 2 0.995012 0.995012 0.02 1 0.887537 0.887537 0.02 2 0.99005 0.99005 0.4 1 0.527089 0.527089 0.4 2 0.818731 0.818731 0.4 3 0.940242 0.940242 0.4 4 0.982477 0.982477 1 1 0.317311 0.317311 1 2 0.606531 0.606531 1 3 0.801252 0.801252 1 4 0.909796 0.909796 1 5 0.962566 0.962566 2 3 0.572407 0.572407 3 3 0.391625 0.391625 4 3 0.261464 0.261464 5 3 0.171797 0.171797 6 3 0.11161 0.11161 1 10 0.999828 0.999828 2 10 0.99634 0.99634 3 10 0.981424 0.981424 cumchn_test CUMCHN computes the cumulative density function for the noncentral chi-squared distribution. CHI_NONCENTRAL_CDF_VALUES looks up some values. DF Lambda X CDF CDF (Lookup) (Computed) 1 0.5 3 0.839944 0.839944 2 0.5 3 0.695906 0.695906 3 0.5 3 0.535088 0.535088 1 1 3 0.764784 0.764784 2 1 3 0.620644 0.620644 3 1 3 0.469167 0.469167 1 5 3 0.307088 0.307088 2 5 3 0.220382 0.220382 3 5 3 0.150025 0.150025 1 20 3 0.00307116 0.00307116 2 20 3 0.00176398 0.00176398 3 20 3 0.000981679 0.000981679 60 30 60 0.0165175 0.0165175 80 30 60 0.000202342 0.000202341 100 30 60 4.98448e-07 4.98446e-07 1 5 0.05 0.0151325 0.0151325 2 5 0.05 0.00209041 0.00209041 3 5 0.05 0.000246502 0.000246502 10 2 4 0.0263684 0.0263683 10 3 4 0.0185798 0.0185798 10 4 4 0.0130574 0.0130574 10 2 5 0.0583804 0.0583804 10 3 5 0.0424978 0.0424978 10 4 5 0.0308214 0.0308214 10 2 6 0.105788 0.105788 10 3 6 0.0794084 0.0794084 10 4 6 0.0593201 0.0593201 DF Lambda X 1-CDF CCDF (Lookup) (Computed) 1 0.5 3 0.160056 0.160056 2 0.5 3 0.304094 0.304094 3 0.5 3 0.464912 0.464912 1 1 3 0.235216 0.235216 2 1 3 0.379356 0.379356 3 1 3 0.530833 0.530833 1 5 3 0.692912 0.692912 2 5 3 0.779618 0.779618 3 5 3 0.849975 0.849975 1 20 3 0.996929 0.996929 2 20 3 0.998236 0.998236 3 20 3 0.999018 0.999018 60 30 60 0.983483 0.983483 80 30 60 0.999798 0.999798 100 30 60 1 1 1 5 0.05 0.984868 0.984867 2 5 0.05 0.99791 0.99791 3 5 0.05 0.999753 0.999753 10 2 4 0.973632 0.973632 10 3 4 0.98142 0.98142 10 4 4 0.986943 0.986943 10 2 5 0.94162 0.94162 10 3 5 0.957502 0.957502 10 4 5 0.969179 0.969179 10 2 6 0.894212 0.894212 10 3 6 0.920592 0.920592 10 4 6 0.94068 0.94068 cumf_test CUMF computes the F CDF and the complementary CDF. F_CDF_VALUES looks up some values. X DFN DFD CDF CDF (Lookup) (Computed) 1 1 1 0.5 0.5 0.528 1 5 0.499971 0.499971 1.89 5 1 0.499603 0.499603 1.69 1 5 0.749699 0.749699 1.6 2 10 0.750466 0.750466 1.47 4 20 0.751416 0.751416 4.06 1 5 0.899987 0.899987 3.05 6 6 0.899713 0.899713 2.09 8 16 0.900285 0.900285 6.61 1 5 0.950025 0.950025 3.71 3 10 0.950057 0.950057 3 6 12 0.950193 0.950193 10.01 1 5 0.975013 0.975013 16.26 1 5 0.990002 0.990002 22.78 1 5 0.994998 0.994998 47.18 1 5 0.999 0.999 1 2 5 0.568799 0.568799 1 3 5 0.535145 0.535145 1 4 5 0.514343 0.514343 1 5 5 0.5 0.5 X DFN DFD 1-CDF CCDF (Lookup) (Computed) 1 1 1 0.5 0.5 0.528 1 5 0.500029 0.500029 1.89 5 1 0.500397 0.500397 1.69 1 5 0.250301 0.250301 1.6 2 10 0.249534 0.249534 1.47 4 20 0.248584 0.248584 4.06 1 5 0.100013 0.100013 3.05 6 6 0.100287 0.100287 2.09 8 16 0.099715 0.0997154 6.61 1 5 0.049975 0.0499751 3.71 3 10 0.049943 0.0499425 3 6 12 0.049807 0.0498074 10.01 1 5 0.024987 0.0249866 16.26 1 5 0.009998 0.00999777 22.78 1 5 0.005002 0.00500222 47.18 1 5 0.001 0.00100004 1 2 5 0.431201 0.431201 1 3 5 0.464855 0.464855 1 4 5 0.485657 0.485657 1 5 5 0.5 0.5 cumfnc_test CUMFNC computes the noncentral F CDF and the complementary CDF. F_NONCENTRAL_CDF_VALUES looks up some values. X DFN DFD LAMBDA CDF CDF (Lookup) (Computed) 1 1 1 0 0.5 0.5 1 1 5 0 0.636783 0.636783 1 1 5 0.25 0.584092 0.584092 0.5 1 5 1 0.323443 0.323443 1 1 5 1 0.450119 0.450119 2 1 5 1 0.607888 0.607887 3 1 5 1 0.705928 0.705927 4 1 5 1 0.772178 0.772178 5 1 5 1 0.819105 0.819104 1 1 5 2 0.317035 0.317035 1 2 5 1 0.432722 0.432721 1 2 10 1 0.45027 0.450269 1 3 5 1 0.426188 0.426188 1 3 5 2 0.337744 0.337744 1 4 5 1 0.422911 0.422911 2 4 5 1 0.692767 0.692765 1 5 1 0 0.363217 0.363217 1 5 5 1 0.421005 0.421005 1 6 6 1 0.426667 0.426667 1 6 12 1 0.446402 0.446401 2 8 16 1 0.844589 0.844584 2 16 8 1 0.816368 0.816367 X DFN DFD LAMBDA 1-CDF CCDF (Lookup) (Computed) 1 1 1 0 0.5 0.5 1 1 5 0 0.363217 0.363217 1 1 5 0.25 0.415908 0.415908 0.5 1 5 1 0.676557 0.676557 1 1 5 1 0.549881 0.549881 2 1 5 1 0.392112 0.392113 3 1 5 1 0.294072 0.294073 4 1 5 1 0.227822 0.227822 5 1 5 1 0.180895 0.180896 1 1 5 2 0.682965 0.682965 1 2 5 1 0.567278 0.567279 1 2 10 1 0.54973 0.549731 1 3 5 1 0.573812 0.573812 1 3 5 2 0.662256 0.662256 1 4 5 1 0.577089 0.577089 2 4 5 1 0.307233 0.307235 1 5 1 0 0.636783 0.636783 1 5 5 1 0.578995 0.578995 1 6 6 1 0.573333 0.573333 1 6 12 1 0.553598 0.553599 2 8 16 1 0.155411 0.155416 2 16 8 1 0.183632 0.183633 cumgam_test CUMGAM computes the Gamma CDF and the complementary CDF. GAMMA_INC_VALUES looks up some values. A X CDF CDF (Lookup) (Computed) 0.1 0.0316228 0.742026 0.742026 0.1 0.316228 0.911975 0.911975 0.1 1.58114 0.989896 0.989896 0.5 0.0707107 0.293128 0.293128 0.5 0.707107 0.765642 0.765642 0.5 3.53553 0.992166 0.992166 1 0.1 0.0951626 0.0951626 1 1 0.632121 0.632121 1 5 0.993262 0.993262 1.1 0.104881 0.0757471 0.0757471 1.1 1.04881 0.607646 0.607646 1.1 5.24404 0.993343 0.993342 2 0.141421 0.0091054 0.00910536 2 1.41421 0.413064 0.413064 2 7.07107 0.993145 0.993145 6 2.44949 0.0387318 0.0387318 6 12.2474 0.982594 0.982594 11 16.5831 0.940427 0.940427 26 25.4951 0.486387 0.486387 41 44.8219 0.735971 0.735971 A X CDF CDF (Lookup) (Computed) 0.1 0.0316228 0.257974 0.257974 0.1 0.316228 0.0880247 0.0880247 0.1 1.58114 0.0101045 0.0101045 0.5 0.0707107 0.706872 0.706872 0.5 0.707107 0.234358 0.234358 0.5 3.53553 0.0078339 0.00783386 1 0.1 0.904837 0.904837 1 1 0.367879 0.367879 1 5 0.0067379 0.00673795 1.1 0.104881 0.924253 0.924253 1.1 1.04881 0.392354 0.392354 1.1 5.24404 0.0066575 0.00665752 2 0.141421 0.990895 0.990895 2 1.41421 0.586936 0.586936 2 7.07107 0.006855 0.00685497 6 2.44949 0.961268 0.961268 6 12.2474 0.0174063 0.0174063 11 16.5831 0.0595733 0.0595733 26 25.4951 0.513613 0.513613 41 44.8219 0.264029 0.264029 cumnbn_test(): cumnbn() computes the Negative Binomial CDF. negative_binomial_cdf_values() looks up some values. F S Pr CDF CDF (Lookup) (Computed) 4 4 0.5 0.6367 0.636719 3 5 0.5 0.3633 0.363281 2 6 0.5 0.1445 0.144531 3 4 0.5 0.5 0.5 2 5 0.5 0.2266 0.226563 1 6 0.5 0.0625 0.0625 2 4 0.5 0.3438 0.34375 1 5 0.5 0.1094 0.109375 0 6 0.5 0.0156 0.015625 2 4 0.4 0.1792 0.1792 1 5 0.4 0.041 0.04096 0 6 0.4 0.0041 0.004096 2 4 0.3 0.0705 0.07047 1 5 0.3 0.0109 0.010935 0 6 0.3 0.0007 0.000729 11 1 0.3 0.9862 0.986159 10 2 0.3 0.915 0.914975 9 3 0.3 0.7472 0.747185 17 1 0.1 0.8499 0.849905 16 2 0.1 0.5497 0.549716 15 3 0.1 0.2662 0.266204 9 1 0.1 0.6513 0.651322 8 2 0.1 0.2639 0.263901 7 3 0.1 0.0702 0.0701908 2 0 0.01 1 1 1 1 0.01 0.0199 0.0199 0 2 0.01 0.0001 0.0001 F S Pr 1-CDF CCDF (Lookup) (Computed) 4 4 0.5 0.3633 0.363281 3 5 0.5 0.6367 0.636719 2 6 0.5 0.8555 0.855469 3 4 0.5 0.5 0.5 2 5 0.5 0.7734 0.773437 1 6 0.5 0.9375 0.9375 2 4 0.5 0.6562 0.65625 1 5 0.5 0.8906 0.890625 0 6 0.5 0.9844 0.984375 2 4 0.4 0.8208 0.8208 1 5 0.4 0.959 0.95904 0 6 0.4 0.9959 0.995904 2 4 0.3 0.9295 0.92953 1 5 0.3 0.9891 0.989065 0 6 0.3 0.9993 0.999271 11 1 0.3 0.0138 0.0138413 10 2 0.3 0.085 0.085025 9 3 0.3 0.2528 0.252815 17 1 0.1 0.1501 0.150095 16 2 0.1 0.4503 0.450284 15 3 0.1 0.7338 0.733796 9 1 0.1 0.3487 0.348678 8 2 0.1 0.7361 0.736099 7 3 0.1 0.9298 0.929809 2 0 0.01 0 0 1 1 0.01 0.9801 0.9801 0 2 0.01 0.9999 0.9999 cumnor_test CUMNOR computes the Normal CDF and the complementary CDF. NORMAL_CDF_VALUES looks up some values. X CDF CDF (Lookup) (Computed) 0 0.5 0.5 0.1 0.539828 0.539828 0.2 0.57926 0.57926 0.3 0.617911 0.617911 0.4 0.655422 0.655422 0.5 0.691462 0.691462 0.6 0.725747 0.725747 0.7 0.758036 0.758036 0.8 0.788145 0.788145 0.9 0.81594 0.81594 1 0.841345 0.841345 1.5 0.933193 0.933193 2 0.97725 0.97725 X 1-CDF CCDF (Lookup) (Computed) 0 0.5 0.5 0.1 0.460172 0.460172 0.2 0.42074 0.42074 0.3 0.382089 0.382089 0.4 0.344578 0.344578 0.5 0.308538 0.308538 0.6 0.274253 0.274253 0.7 0.241964 0.241964 0.8 0.211855 0.211855 0.9 0.18406 0.18406 1 0.158655 0.158655 1.5 0.0668072 0.0668072 2 0.0227501 0.0227501 cumpoi_test CUMPOI computes the Poisson CDF and the complementary CDF. POISSON_CDF_VALUES looks up some values. X LAMBDA CDF CDF (Lookup) (Computed) 0 0.02 0.98 0.980199 0 0.1 0.905 0.904837 1 0.1 0.995 0.995321 0 0.5 0.607 0.606531 1 0.5 0.91 0.909796 2 0.5 0.986 0.985612 0 1 0.368 0.367879 1 1 0.736 0.735759 2 1 0.92 0.919699 3 1 0.981 0.981012 0 2 0.135 0.135335 1 2 0.406 0.406006 2 2 0.677 0.676676 3 2 0.857 0.857123 0 5 0.007 0.00673795 1 5 0.04 0.0404277 2 5 0.125 0.124652 3 5 0.265 0.265026 4 5 0.441 0.440493 5 5 0.616 0.615961 6 5 0.762 0.762183 X LAMBDA 1-CDF CCDF (Lookup) (Computed) 0 0.02 0.02 0.0198013 0 0.1 0.095 0.0951626 1 0.1 0.005 0.00467884 0 0.5 0.393 0.393469 1 0.5 0.09 0.090204 2 0.5 0.014 0.0143877 0 1 0.632 0.632121 1 1 0.264 0.264241 2 1 0.08 0.0803014 3 1 0.019 0.0189882 0 2 0.865 0.864665 1 2 0.594 0.593994 2 2 0.323 0.323324 3 2 0.143 0.142877 0 5 0.993 0.993262 1 5 0.96 0.959572 2 5 0.875 0.875348 3 5 0.735 0.734974 4 5 0.559 0.559507 5 5 0.384 0.384039 6 5 0.238 0.237817 cumt_test CUMT computes the Student T CDF and the complementary CDF. STUDENT_CDF_VALUES looks up some values. X DF CDF CDF (Lookup) (Computed) 0.325 1 0.6 0.600023 0.289 2 0.6 0.600108 0.277 3 0.6 0.600115 0.271 4 0.6 0.6001 0.267 5 0.6 0.599934 0.816 2 0.75 0.749886 0.727 5 0.75 0.750088 2.92 2 0.95 0.95 2.015 5 0.95 0.949997 6.965 2 0.99 0.990001 4.541 3 0.99 0.990002 3.747 4 0.99 0.99 3.365 5 0.99 0.990001 X DF 1-CDF CCDF (Lookup) (Computed) 0.325 1 0.4 0.399977 0.289 2 0.4 0.399892 0.277 3 0.4 0.399885 0.271 4 0.4 0.3999 0.267 5 0.4 0.400066 0.816 2 0.25 0.250114 0.727 5 0.25 0.249912 2.92 2 0.05 0.0499996 2.015 5 0.05 0.0500031 6.965 2 0.01 0.00999877 4.541 3 0.01 0.00999824 3.747 4 0.01 0.00999954 3.365 5 0.01 0.00999924 error_f_test ERROR_F computes the error function ERF; ERROR_FC the complementary error function ERFC. ERF_VALUES looks up some values. X ERF ERF (Lookup) (Computed) 0 0 0 0.1 0.112463 0.112463 0.2 0.222703 0.222703 0.3 0.328627 0.328627 0.4 0.428392 0.428392 0.5 0.5205 0.5205 0.6 0.603856 0.603856 0.7 0.677801 0.677801 0.8 0.742101 0.742101 0.9 0.796908 0.796908 1 0.842701 0.842701 1.1 0.880205 0.880205 1.2 0.910314 0.910314 1.3 0.934008 0.934008 1.4 0.952285 0.952285 1.5 0.966105 0.966105 1.6 0.976348 0.976348 1.7 0.98379 0.98379 1.8 0.989091 0.989091 1.9 0.99279 0.99279 2 0.995322 0.995322 X ERFC ERFC (Lookup) (Computed) 0 1 1 0.1 0.887537 0.887537 0.2 0.777297 0.777297 0.3 0.671373 0.671373 0.4 0.571608 0.571608 0.5 0.4795 0.4795 0.6 0.396144 0.396144 0.7 0.322199 0.322199 0.8 0.257899 0.257899 0.9 0.203092 0.203092 1 0.157299 0.157299 1.1 0.119795 0.119795 1.2 0.089686 0.089686 1.3 0.0659921 0.0659921 1.4 0.0477149 0.0477149 1.5 0.0338949 0.0338949 1.6 0.0236516 0.0236516 1.7 0.0162095 0.0162095 1.8 0.0109095 0.0109095 1.9 0.00720957 0.00720957 2 0.00467774 0.00467773 gamma_x_test GAMMA_X computes the Gamma function; tgamma() computes the Gamma function (math library); GAMMA_VALUES looks up some values. X GAMMA tgamma GAMMA_X (Lookup) (Computed) 0.2 4.59084 4.59084 4.59084 0.4 2.21816 2.21816 2.21816 0.6 1.48919 1.48919 1.48919 0.8 1.16423 1.16423 1.16423 1 1 1 1 1.1 0.951351 0.951351 0.951351 1.2 0.918169 0.918169 0.918169 1.3 0.897471 0.897471 0.897471 1.4 0.887264 0.887264 0.887264 1.5 0.886227 0.886227 0.886227 1.6 0.893515 0.893515 0.893515 1.7 0.908639 0.908639 0.908639 1.8 0.931384 0.931384 0.931384 1.9 0.961766 0.961766 0.961766 2 1 1 1 10 362880 362880 362880 20 1.21645e+17 1.21645e+17 1.21645e+17 30 8.84176e+30 8.84176e+30 8.84176e+30 gamma_inc_test GAMMA_INC evaluates the incomplete Gamma ratio; GAMMA_INC_INV inverts it. Parameters: A = 3 X P Q Inverse 0 0 1 0 0.1 0.000154653 0.999845 0.1 0.2 0.00114848 0.998852 0.2 0.3 0.00359949 0.996401 0.3 0.4 0.00792633 0.992074 0.4 0.5 0.0143877 0.985612 0.5 0.6 0.0231153 0.976885 0.6 0.7 0.0341416 0.965858 0.7 0.8 0.0474226 0.952577 0.8 0.9 0.0628569 0.937143 0.9 1 0.0803014 0.919699 1 psi_test PSI computes the Psi function; PSI_VALUES looks up some values. X PSI PSI (Lookup) (Computed) 1 -0.577216 -0.577216 1.1 -0.423755 -0.423755 1.2 -0.28904 -0.28904 1.3 -0.169191 -0.169191 1.4 -0.0613845 -0.0613845 1.5 -0.03649 0.03649 1.6 0.126047 0.126047 1.7 0.208548 0.208548 1.8 0.284991 0.284991 1.9 0.356184 0.356184 2 0.422784 0.422784 cdflib_test() Normal end of execution. 05 May 2021 08:15:27 AM