Abstract
This paper proposes the new three-parameter type I half-logistic inverse Weibull (TIHLIW) distribution which generalizes the inverse Weibull model. The density function of the TIHLIW can be expressed as a linear combination of the inverse Weibull densities. Some mathematical quantities of the proposed TIHLIW model are derived. Four estimation methods, namely, the maximum likelihood, least squares, weighted least squares, and Cramér–von Mises methods, are utilized to estimate the TIHLIW parameters. Simulation results are presented to assess the performance of the proposed estimation methods. The importance of the TIHLIW model is studied via a real data application.
Highlights
Introduction e inverseWeibull (IW) distribution is known as reciprocal Weibull distribution
We compare the performances of the maximum likelihood estimators (MLEs), least squares estimators (LSEs), weighted least squares estimators (WLSEs), and Cramer–von Mises estimators (CVMEs) based on the mean square errors (MSEs) for different sample sizes
E fitted probability density function (PDF), estimated cumulative distribution function (CDF), estimated survival function (SF), and PP plots of the type I half-logistic inverse Weibull (TIHLIW) distribution are shown in Figures 2 and 3
Summary
We studied some statistical properties of the TIHLIW distribution, such as quantile function, ordinary moments, moment generating function, incomplete moment, and mean deviation. E associated components of the score vector zl zl zl T. where (Ai 1) in the case of LSEs and (Ai ((n + 1)2(n + 2))/(i(n − i + 1))) in the case of WLSEs. Further, the LSEs and WLSEs of the TIHLIW parameters are obtained by solving the following nonlinear equations simultaneously with respect to α, λ, and β: zS(α, λ, β) n ⎧⎪⎪⎪⎨ 1 − 1 − e − αx−(iβ) λ i ⎫⎪⎪⎪⎬. Let x(1) < x(2) < · · · < x(n) be the order statistics of a sample from the TIHLIW distribution, and the LSEs and WLSEs of α, λ, and β can be obtained by minimizing the following function with respect to α, λ, and β: 4.3. Where φ1i, φ2i, and φ3i are, respectively, defined in equations (47)–(49)
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