exponential_inverse_cdf

Evaluates the inverse of the exponential cumulative distribution function (CDF).

Synopsis

#include<imsls.h>

float imsls_f_exponential_inverse_cdf(floatp, floatb)

The type double function is imsls_d_exponential_inverse_cdf.

Required Arguments

floatp (Input)
Probability for which the inverse of the exponential CDF is to be evaluated. p must lie in the closed interval [0, 1].

floatb (Input)
Scale parameter of the exponential CDF. b must be positive.

Return Value

Function value, the value of the inverse of the exponential CDF. A value of NaN is returned if an input value is in error.

Description

The function imsls_f_exponential_inverse_cdf(p, b) evaluates F-1(p∣b), the inverse CDF of an exponential random variable with probability argument p = p and scale parameter b = b:

F-1(p∣b) = -blog(1-p)

The probability that an exponential random variable takes a value less than or equal to the returned value is p.

Example

In this example, we evaluate the exponential inverse CDF at p = 0.8647, b = 1.0.:

 

#include <imsls.h>

#include <stdio.h>

 

int main()

{

float p = 0.8647;

float b = 1.0;

float x;

 

x = imsls_f_exponential_inverse_cdf(p, b);

printf("The probability that exponential random ");

printf("variable X with\nscale parameter b = ");

printf("%3.1f is less than or equal to %6.4f", b, x);

printf("\nis %6.4f\n\n", p);

}

Output

The probability that exponential random variable X with

scale parameter b = 1.0 is less than or equal to 2.0003

is 0.8647