Abstract
In this paper, we develop some goodness of fit tests for Rayleigh distribution based on Phi-divergence. Using Monte Carlo simulation, we compare the power of the proposed tests with some traditional goodness of fit tests including Kolmogorov-Smirnov, Anderson-Darling and Cramer von-Mises tests. The results indicate that the proposed tests perform well as compared with their competing tests in the literature. Finally, the proposed procedures are illustrated via a real data set.
Highlights
A continuous random variable X is said to have Rayleigh distribution with location parameter μ ∈ R, and scale parameter σ > 0, denoted by X ∼ Ra (μ, σ), if its probability distribution function is given by f0(x, μ, σ) = x − σ2 μ e− (x−μ)2 2σ2, x ≥ μ, (1)with the corresponding cumulative distribution function F0
This paper introduces some goodness of t tests for Rayleigh distribution when the location parameter μ is known and the scale parameter σ is unknown
In order to compare the power of dierent goodness of t tests, we generated 50,000 simple random samples of sizes n = 10, 20 and 50 under 14 alternative distributions considered by Best et al (2010)
Summary
A continuous random variable X is said to have Rayleigh distribution with location parameter μ ∈ R, and scale parameter σ > 0, denoted by X ∼ Ra (μ, σ), if its probability distribution function (pdf) is given by f0(x, μ, σ). The Rayleigh distribution was rstly motivated with a problem in acoustics, and has been utilized for modelling the distribution of the distance between two individuals in a Poisson process. This distribution typically arises when overall size of a vector is related to its directional components. It is well-known that if Z and W are two independent and identical random variables fro√m a standard normal distribution with mean zero and variance σ2, X = Z2 + W 2 follows a Rayleigh. This paper introduces some goodness of t tests for Rayleigh distribution when the location parameter μ is known and the scale parameter σ is unknown.
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