Different methods of estimation for the parameters of half logistic Lomax distribution

Aldahlan, Maha A.

doi:10.12988/ams.2019.9116

Cited by 2 publications

(2 citation statements)

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“….)). Thus, many studies used the HL-G family to introduce new flexible continuous distributions with modelling perspectives, such as [25] with the HL Lomax (HLL) distribution, [26] in which different methods of estimation for the HLL distribution are proposed, ref. [27] with the HL power Lindley (HLPL) distribution, [28] with the HL generalized Weibull (HLGW) distribution, [29] with the HL Burr X (HLBX) distribution and [30] which studied different estimation methods for the HL Topp-Leone (HLTP) distribution.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Almarashi

Badr

Elgarhy

et al. 2020

Entropy

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The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.Entropy 2020, 22, 449 2 of 24 respectively, where α is a scale parameter. As notable features, the IR distribution has tractable and simple probability functions, is unimodal and right-skewed, and possesses a hazard rate function with a singular curvature: it increases at a certain value, then decreases until attain a kind of stabilization. The pioneer studies are [2] which presents some properties of the maximum likelihood estimator of α, and [3] which provides closed-form expressions for the (standard) mean, harmonic mean, geometric mean, mode and median of the IR distribution. Also, among the amount of works investigating the statistical aspects of the IR distribution, the reader can be referred to [4][5][6][7][8][9][10][11][12].In the recent years, several extensions of the IR distribution were developed, using different mathematical techniques, often at the basis of general families of distributions. Among them, there are the beta IR (BIR) distribution by [13], transmuted IR (TIR) distribution by [14], modified IR (MIR) distribution by [15], transmuted modified IR (TMIR) distribution by [16], transmuted exponentiated IR (TEIR) distribution by [17], Kumaraswamy exponentiated IR (KEIR) distribution by [18], weighted IR (WIR) distribution by [19], odd Fréchet IR (OFIR) distribution by [20], type II Topp-Leone IR (TIITLIR) distribution by [21], type II Topp-Leone generalized IR (TIITLGIR) distribution by [22] and exponentiated IR (EIR) distribution by [23].However, to the best of our knowledge, the use of the half-logistic transformation to extend the IR distribution remains unexplored, despite recent success in this regard. This half-log...

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Section: Introductionmentioning

confidence: 99%

Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Almarashi

Badr

Elgarhy

et al. 2020

Entropy

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“…Recently, statisticians have been very interested in comparing different classical estimation methods for estimating the parameters of several distributions. For example, the generalised Rayleigh (Kundu and Raqab [16]), weighted Lindley (Mazucheli et al [17]), exponentiated-Chen (Dey et al [18]), alpha logarithmic transformed Weibull (Nassar et al [19]), transmuted exponentiated Pareto (Nassar et al [20]), half-logistic Lomax (Aldahlan [21]), quasi xgamma-geometric (Sen et al [22]), Weibull Marshall-Olkin Lindley (Afify et al [23]), logarithmic transformed Weibull (Nassar et al [24]).…”

Section: Introductionmentioning

confidence: 99%

The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

Aldahlan

Afify

2020

Mathematics

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In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution.

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Different methods of estimation for the parameters of half logistic Lomax distribution

Cited by 2 publications

References 14 publications

Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

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