The Half-Logistic Generalized Weibull Distribution

Anwar, Masood; Bibi, Amna

doi:10.1155/2018/8767826

Cited by 12 publications

(12 citation statements)

References 19 publications

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“…A more recent paper by Anwar and Bibi (2018) introduced the three-parameter half-logistic generalized Weibull (HLGW) distribution with CDFFXfalse(xfalse)badbreakafter=1badbreakafter−normalexp⁡false(1badbreakafter−false[1badbreakafter+γxηfalse]ωfalse)1badbreakafter+normalexp⁡false(1badbreakafter−false[1badbreakafter+γxηfalse]ωfalse),0.25emxgoodbreakafter>0,ω,η,γgoodbreakafter>0.…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Anwar and Bibi (2018) applied the HLGW distribution to the waiting time data and the fit of the HLGW distribution was compared with those of six competing one, two, and three-parameter distributions including the Weibull distribution. Based on the results from the distributions fittings in Table 4 of Anwar and Bibi (2018) the HLGW distribution indicate a better performance than the other distributions in modeling the waiting time data. Here, we want to point out that the two-parameter RGD in this paper offers a better fit to the waiting time data than the three-parameter HLGW distribution because the log-likelihood of the RGD (316.9575) is less than that of the HLGW distribution (317.1130).…”

Section: Discussionmentioning

confidence: 99%

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On the Rayleigh-geometric distribution with applications

Okorie

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Ohakwe

et al. 2019

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A two-parameter Rayleigh-geometric distribution with increasing-decreasing-increasing and strictly increasing hazard rate characteristics is reviewed. Various properties are discussed and expressed analytically. The estimation of the distribution parameters is studied by the method of maximum likelihood and validated by a simulation study. Numerical examples based on two real data-sets on the waiting time in queue and CO 2 emissions are given. The Rayleigh-geometric distribution in this paper has a simpler analytical expression compared to the pre-existing distributions with different parameterizations.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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On the Rayleigh-geometric distribution with applications

Okorie

Akpanta

Ohakwe

et al. 2019

Heliyon

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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. That is, attracted by the success of the above extensions, we investigate the half-logistic IR (HLIR) distribution, constituting a new lifetime distribution with two parameters, and a new extension of the IR distribution as well.…”

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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“…That explains why several special members have been recently studied in detail. We refer the reader to [3] for the type I half-logistic Burr XII distribution (also called extended Bur XII distribution), [4] for the type I half-logistic generalized Weibull distribution, [5] for the type I half-logistic Lomax distribution, and [6] for the type I half-logistic exponential distribution. Also, with the use of an additional parameter, the type I half-logistic-G family was recently generalized by [7].…”

Section: Introductionmentioning

confidence: 99%

Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution

et al. 2019

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In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution.

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The Half-Logistic Generalized Weibull Distribution

Cited by 12 publications

References 19 publications

On the Rayleigh-geometric distribution with applications

On the Rayleigh-geometric distribution with applications

Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution

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