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Rayleigh cumulative distribution function


p = raylcdf(x,b)
p = raylcdf(x,b,'upper')


p = raylcdf(x,b) returns the Rayleigh cdf at each value in x using the corresponding scale parameter, b. x and b can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input for x or b is expanded to a constant array with the same dimensions as the other input.

p = raylcdf(x,b,'upper') returns the complement of the Rayleigh cdf at each value in x, using an algorithm that more accurately computes the extreme upper tail probabilities.

The Rayleigh cdf is



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Compute the cdf of a Rayleigh distribution with parameter B = 1.

x = 0:0.1:3;
p = raylcdf(x,1);

Plot the cdf.


Figure contains an axes object. The axes object contains an object of type line.


[1] Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. Hoboken, NJ: Wiley-Interscience, 2000. pp. 134–136.

Extended Capabilities

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Version History

Introduced before R2006a