1 #ifndef LIBPROB_H 2 #define LIBPROB_H 3 4 /* cephes error conditions */ 5 enum { 6 CEPHES_DOMAIN = 1, /* argument domain error */ 7 CEPHES_SING, /* argument singularity */ 8 CEPHES_OVERFLOW, /* overflow range error */ 9 CEPHES_UNDERFLOW, /* underflow range error */ 10 CEPHES_TLOSS, /* total loss of precision */ 11 CEPHES_PLOSS, /* partial loss of precision */ 12 CEPHES_UNKNOWN /* unspecified error */ 13 }; 14 15 /* area under the binomial pdf, from 0 to k, of the 16 binomial distribution with success probability p 17 and n trials. 18 */ 19 double bdtr (int k, int n, double p); 20 21 /* area under the binomial pdf, from k+1 to n, of the 22 binomial distribution with success probability p 23 and n trials. 24 */ 25 double bdtrc (int k, int n, double p); 26 27 /* success probability such that the area under the 28 binomial pdf from 0 to k with n trials equals y. 29 */ 30 double bdtri (int k, int n, double y); 31 32 /* Returns the area from 0 to x under the beta density 33 function with parameters a and b 34 */ 35 double btdtr (double a, double b, double x); 36 37 /* area under the left hand tail (from 0 to x) 38 of the Chi square probability density function with 39 v degrees of freedom. 40 */ 41 double chdtr (double v, double x); 42 43 /* area under the right hand tail (from x to infinity) 44 of the Chi square probability density function with 45 v degrees of freedom. 46 */ 47 double chdtrc (double v, double x); 48 49 /* 50 Finds the Chi-square argument x such that the integral 51 from x to infinity of the Chi-square density is equal 52 to the given cumulative probability y. 53 */ 54 double chdtri (double df, double y); 55 56 /* 57 Returns the area from 0 to x under the F density 58 function (also known as Snedcor's density or the 59 variance ratio density). 60 */ 61 double fdtr (double a, double b, double x); 62 63 /* 64 Returns the area from x to infinity under the F density 65 function (also known as Snedcor's density or the 66 variance ratio density). 67 */ 68 double fdtrc (double a, double b, double x); 69 70 /* 71 Finds the F density argument x such that the integral 72 from x to infinity of the F density is equal to the 73 given probability p. 74 */ 75 double fdtri (double a, double b, double y); 76 77 /* 78 Computes the integral from minus infinity to t of the Student 79 t distribution with k > 0 degrees of freedom. 80 */ 81 double stdtr (double rk, double t); 82 83 /* 84 Given probability p, finds the argument t such that stdtr(k,t) 85 is equal to p. 86 */ 87 double stdtri (double rk, double p); 88 89 /* 90 Returns the area under the Gaussian probability density 91 function, integrated from minus infinity to x. 92 */ 93 double ndtr (double a); 94 95 /* 96 Returns the argument, x, for which the area under the 97 Gaussian probability density function (integrated from 98 minus infinity to x) is equal to y. 99 */ 100 double ndtri (double y0); 101 102 /* 103 Returns the sum of the first k terms of the Poisson 104 distribution with mean and variance m. 105 */ 106 double pdtr (int k, double m); 107 108 /* 109 Returns the sum of the terms k+1 to infinity of the Poisson 110 distribution with mean and variance m. 111 */ 112 double pdtrc (int k, double m); 113 114 /* 115 Finds the Poisson variable x such that the integral 116 from 0 to x of the Poisson density is equal to the 117 given probability y. 118 */ 119 double pdtri (int k, double y); 120 121 /* Returns the integral from zero to x of the gamma pdf 122 with XX. 123 */ 124 double gdtr (double a, double b, double x); 125 126 /* Returns the integral from x to infinity of the gamma 127 pdf with XX. 128 */ 129 double gdtrc (double a, double b, double x); 130 131 /* 132 Returns the inverse incomplete gamma function. 133 */ 134 double igami (double a, double y0 ); 135 136 /* 137 Returns gamma function of the argument. The result is 138 correctly signed. 139 */ 140 double cephes_gamma (double x); /* cephes' gamma(), renamed */ 141 142 /* 143 Returns the base e (2.718...) logarithm of the absolute 144 value of the gamma function of the argument. 145 The sign (+1 or -1) of the gamma function is set in a 146 global variable named cephes_sgngam. 147 */ 148 double cephes_lgamma (double x); /* alias for cephes' lgam() */ 149 150 /* Returns the current value of cephes_sgngam */ 151 int get_cephes_sgngam (void); 152 153 /* Returns incomplete beta integral of the arguments, evaluated 154 from zero to x 155 */ 156 double incbet (double a, double b, double x); 157 158 /* Returns the Psi (digamma) function of the argument */ 159 double psi (double x); 160 161 /* Evaluate roots of polynomial */ 162 int polrt (double *xcof, double *cof, int m, cmplx *root); 163 164 /* Gauss hypergeometric function 2F1 */ 165 double hyp2f1 (double a, double b, double c, double x); 166 167 /* Accessor for cephes error code */ 168 int get_cephes_errno (void); 169 170 void set_cephes_hush (int s); 171 172 #endif /* LIBPROB_H */ 173