RALDF

This function evaluates the Rayleigh cumulative distribution function.

Function Return Value

RALDF — Function value, the probability that a Rayleigh random variable takes a value less than or equal to X. (Output)

Required Arguments

X — Argument for which the Rayleigh cumulative distribution function is to be evaluated. (Input)

ALPHA — Scale parameter of the Rayleigh cumulative distribution function. (Input)

FORTRAN 90 Interface

Generic: RALDF (X, ALPHA)

Specific: The specific interface names are S_RALDF and D_RALDF.

FORTRAN 77 Interface

Single: RALDF (X, ALPHA)

Double: The double precision name is DRALDF.

Description

The function RALDF evaluates the Rayleigh cumulative probability distribution function, which is a special case of the Weibull cumulative probability distribution function, where the shape parameter GAMMA is 2.0

 

RALDF evaluates the Rayleigh cumulative probability distribution function using the relationsip

RALDF (X, ALPHA) = WBLDF(X, SQRT(2.0)*ALPHA, 2.0).

Example

In this example, we evaluate the Rayleigh cumulative distribution function at X = 0.25, ALPHA = 0.5.

 

USE UMACH_INT

USE RALDF_INT

IMPLICIT NONE

INTEGER NOUT

REAL X, ALPHA, PR

CALL UMACH(2, NOUT)

X = 0.25

ALPHA = 0.5

PR = RALDF(X, ALPHA)

WRITE (NOUT, 99999) X, ALPHA, PR

99999 FORMAT (' RALDF(', F4.2, ', ', F4.2, ') = ', F6.4)

END

Output

 

RALDF(0.25, 0.50) = 0.1175