Abstract
In this paper, the applications of the half logistic-Marshall Olkin X family of distributions are investigated with special emphasis to the half logistic-Marshall Olkin Lomax distribution. The specific areas we concentrated are time series modeling, acceptance sampling plan and stress-strength analysis. Different autoregressive minification structures of order one are introduced. The acceptance sampling plan is detailed by considering life time of products following the half logistic-Marshall Olkin Lomax distribution. The stress-strength reliability of the half logistic-Marshall Olkin Lomax distribution is derived and estimated. A simulation study is carried out to examine the bias, mean square error, average confidence length and coverage probability of the maximum likelihood estimator of thestress-strength reliability. Finally a real-life data analysis has also been presented.
Highlights
Many real life phenomena are well described by statistical distributions
Theorem 2.4 stated below is a particaular case of Theorem 2.3, that is it gives a first order autoregressive minification process with marginals following half logistic-Marshall Olkin Lomax (HLMOL)(1, α, θ, β) distribution
Suppose x1, x2, ..., xm is a random sample of size m from the HLMOL distribution with parameters λ = 1, α, θ and c1, and y1, y2, ..., yn is a random sample of size n from the HLMOL distribution with parameters λ = 1, α, θ and c2, and let α and θ be known
Summary
In case where existing distributions are found inadequate for a phenomenon, new generated classes of distributions are defined to meet the requirements Such extended distributions are proved to be extremely useful for modeling real life situations by many authors. The acceptance sampling plan is an important tool in statistical quality control because it helps manufactures to minimize variability and protect the outgoing quality of their products. For convenience one special model of this family, the half logistic-Marshall Olkin Lomax (HLMOL) distribution, is studied in detail. The CDF of the Lomax distribution is given by With this context the main motivation behind this study is to investigate the diverse applications of the HLMO-X family of distributions in various fields like time series, quality control and reliability.
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