exponential_cdf
Evaluates the exponential cumulative distribution function (CDF).
Synopsis
#include<imsls.h>
floatimsls_f_exponential_cdf(float x, float b)
The type double function is imsls_d_exponential_cdf.
Required Arguments
float x (Input)
Argument for which the exponential CDF is to be evaluated. x must be non-negative.
float b (Input)
Scale parameter of the exponential CDF. b must be positive.
Return Value
The probability that an exponential random variable takes a value less than or equal to x. A value of NaN is returned if an input value is in error.
Description
The function imsls_f_exponential_cdf evaluates the exponential cumulative distribution function (CDF). This function is a special case of the gamma CDF
Setting a=1 and applying the scale parameter b = b yields the exponential CDF
This relationship between the gamma and exponential CDFs is used by imsls_f_exponential_cdf.
Example
In this example, we evaluate the exponential CDF at x = 2.0, b = 1.0.
#include <imsls.h>
#include <stdio.h>
int main()
{
float x = 2.0;
float b = 1.0;
float p;
p = imsls_f_exponential_cdf(x,b);
printf("The probability that exponential random ");
printf("variable X with\nscale parameter b = ");
printf("%3.1f is less than or equal to %3.1f", 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 2.0
is 0.8647
