raylfit

Rayleigh parameter estimates

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Syntax

pHat = raylfit(x)
[pHat,pCI] = raylfit(x)
[pHat,pCI] = raylfit(x,alpha)

Description

pHat = raylfit(x) returns the maximum likelihood estimates (MLEs) of the scale parameter b of the Rayleigh distribution, given the sample data in x.

[pHat,pCI] = raylfit(x) also returns the 95% confidence intervals for the parameter estimates.

[pHat,pCI] = raylfit(x,alpha) specifies the confidence level for the confidence intervals to be 100(1 – alpha)%.

example

Examples

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Open Live Script

Generate 100 random numbers from the Rayleigh distribution with the scale parameter b=3.

rng(0,"twister") % For reproducibility
b = 3;
x = raylrnd(b,100,1);

Find the maximum likelihood estimate and 99% confidence interval for the Rayleigh scale parameter.

[pHat,pCI] = raylfit(x,0.01)
pHat = 
3.2575

pCI = 2×1

    2.8834
    3.7337

pHat is the maximum likelihood estimate, and pCI contains the 99% confidence interval. The value in the first row is the lower bound, and the value in the second row is the upper bound.

Input Arguments

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Sample data, specified as a vector of nonnegative scalar values.

Data Types: single | double

Significance level for the confidence intervals, specified as a scalar in the range [0,1]. The confidence level is 100(1 – alpha)%, where alpha is the probability that the confidence intervals do not contain the true value. You can specify [] for alpha to use its default value of 0.05.

Data Types: single | double

Output Arguments

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Rayleigh b parameter estimate, returned as a numeric scalar.

Confidence intervals for the parameter estimate, returned as a 2-by-1 numeric array. The first row contains lower confidence bound values, and the second row contains upper confidence bound values.

Alternative Functionality

raylfit is a function specific to the Rayleigh distribution. Statistics and Machine Learning Toolbox™ also offers the generic functions mle, fitdist, and paramci and the Distribution Fitter app, which support various probability distributions.

  • mle returns MLEs and the confidence intervals of MLEs for the parameters of various probability distributions. You can specify the probability distribution name or a custom probability density function.

  • Create a RayleighDistribution probability distribution object by fitting the distribution to data using the fitdist function or the Distribution Fitter app. The object property B stores the estimate of the Rayleigh scale parameter. To obtain the confidence interval for the parameter estimate, pass the object to paramci.

References

[1] Johnson, N. L., S. Kotz, and A. W. Kemp. Univariate Discrete Distributions. Hoboken, NJ: Wiley-Interscience, 1993.

Version History

Introduced before R2006a

See Also

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