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 relationship

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

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