function pdf = student_pdf ( x, a, b, c ) %*****************************************************************************80 % %% STUDENT_PDF evaluates the central Student T PDF. % % Formula: % % PDF(X)(A,B,C) = Gamma ( (C+1)/2 ) / % ( Gamma ( C / 2 ) * Sqrt ( PI * C ) % * ( 1 + ((X-A)/B)**2/C )**(C + 1/2 ) ) % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 02 November 2005 % % Author: % % John Burkardt % % Parameters: % % Input, real X, the argument of the PDF. % % Input, real A, B, shape parameters of the PDF, % used to transform the argument X to a shifted and scaled % value Y = ( X - A ) / B. It is required that B be nonzero. % For the standard distribution, A = 0 and B = 1. % % Input, real C, is usually called the number of % degrees of freedom of the distribution. C is typically an % integer, but that is not essential. It is required that % C be strictly positive. % % Output, real PDF, the value of the PDF. % y = ( x - a ) / b; pdf = gamma ( 0.5 * ( c + 1.0 ) ) / ( sqrt ( pi * c ) * gamma ( 0.5 * c ) ... * sqrt ( ( 1.0 + y * y / c )^( 2 * c + 1.0 ) ) ); return end