Abstract
A new univariate extension of the Inverse Rayleigh distribution is proposed and studied. Some of its fundamental statistical properties such as some stochastic properties, ordinary and incomplete moments, moments generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering, Rényi, Shannon and q-entropies are derived. A simple type Copula based construction via Morgenstern family and via Claytoncopula is employed to derive many bivariate and multivariate extensions of the new model. We assessed the performance of the maximum likelihood estimators using a simulation study. The importance of the new model is shown via two applications to real data sets.
Highlights
Introduction and motivationA rv W is said to have the Inverse Rayleigh (IR) distribution if its probability density function (PDF), cumulative distribution function (CDF) are given by hλ(ω) =λ2 ω3 exp(−λ2ω−2), [1] andHλ(ω) = exp(−λ2ω−2). [2]The cumulative distribution function (CDF) and probability density function (PDF) of the Generalized Odd Generalized Exponential G (GOGE-G) family are given, respectively, by Fα,β (ω) {1 −
Plots of the GOGEIR hazard rate function (HRF) at some parameters value are presented in Figure 2 to show the flexibility of the new model
Another alternative method for deriving the moment generating function (MGF) can be introduced by the Wright generalized hypergeometric function (WHGF) which is defined by
Summary
A rv W is said to have the Inverse Rayleigh (IR) distribution if its probability density function (PDF), cumulative distribution function (CDF) are given by hλ(ω). Plots of the GOGEIR HRF at some parameters value are presented in Figure 2 to show the flexibility of the new model. The mean of W , variance (V (W) ) skewness (S (W) ) and kurtosis (K (W) ) measures can be calculated from the ordinary moments using well-known relationships. The mean, variance, skewness and kurtosis of the GOGEIR distribution are computed numerically for some selected values using the R software. The first incomplete moment can be calculated by stting r = 1 in φr(t) as φ1(t) Another alternative method for deriving the MGF can be introduced by the Wright generalized hypergeometric function (WHGF) which is defined by (τ)Ψ(u). Equations [9] and [11] can be evaluated by scripts of the Maple, Matlab and Mathematica platforms
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