The Beta Generalized Inverse Weibull Distribution

In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliability function, and hazard function are studied. Next, we derived the quantile function, median, mode, moments, harmonic mean, skewness, and kurtosis. In addition, the order statistics and the mean deviations about the mean and median are found. Other important properties including entropy (Rényi and Shannon), which is a measure of the uncertainty for this distribution, are also investigated. Maximum likelihood estimation is adopted to the model. A simulation study is conducted to estimate the parameters. Four real-life data sets from difference fields were applied on this model. In addition, a comparison between the new model and some competitive models is done via information criteria. Our model shows the best fitting for the real data.

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“…Therefore, it has to be solved numerically. The mode of the BGIRD can be obtained by solving (18) numerically using the Newton-Raphson method.…”

Section: Modementioning

confidence: 99%

“…We shall compare the fit of the proposed BGIRD (and its sub-model namely: BIRD) with several other competitive models namely: the beta generalized inverse Weibull distribution (BGIWD) [18], and exponential, Lindley, and Akash distributions [17] with corresponding cumulative distribution functions (for x > 0) as follows…”

Section: Applicationmentioning

confidence: 99%

A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications

Bakoban

Al-Shehri

2021

Symmetry

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“…For many years, researchers have been developing various extensions and modified forms of the inverse Weibull distribution. Recently, [2] introduced an extension of the inverse Weibull distribution called the beta generalized inverse Weibull distribution. [5] defined a three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate.…”

Section: Introductionmentioning

confidence: 99%

The Exponentiated Kumaraswamy InverseWeibull Distribution with Application in Survival Analysis

Rodrigues¹,

Silva²,

Hamedani³

2016

JSTA

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In this paper, a new distribution called the exponentiated Kumaraswamy inverse Weibull is proposed. This distribution includes as special cases the inverse exponential, inverse Weibull, inverse Rayleigh and exponentiated inverse Weibull distributions. We study the main properties of this distribution, with special emphasis on its moments and some characteristics related to reliability studies. We also discuss parameter estimation considering the methods of moments and maximum likelihood. An application reveals that the model proposed can be very useful in fitting real data.

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“…The IWD has been further studied by Calabria and Pulcini (1990), Khan, Pasha and Pasha (2008), Pawlas and Szynal (2000), Mahmoud, Sultan and Amer (2003) and Elshahat and Ismail (2014). Certain other re-parametric versions of the IWD are proposed in the literature recently by authors like de Gusmão, Ortega and Cordeiro (2011), Khan and King (2012), Khan (2010) and Baharith, Mousa, Atallah and Elgayar (2014). All these families of distributions possess decreasing/upside down bathtub-shaped hazard rate functions.…”

mentioning

confidence: 99%

“…Hanook, Shahbaz, Mohsin and Kibria, 2013), the beta generalised inverse Weibull distribution (BGIWD) (cf. Baharith et al, 2014) etc. Above all, compared to these extended inverse Weibull models, the IKD possess some useful properties as discussed in Section 2 of the paper.…”

mentioning

confidence: 99%

Inverse Kies distribution: Properties and applications

Kumar

Dharmaja²

2022

SASJ

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In this paper, a new class of distribution namely “the inverse Kies distribution” is proposed and some of its important aspects are studied by deriving expressions for its percentile measures, raw moments, reliability measures etc. The maximum likelihood estimation of the parameters of the distribution is discussed and the distribution has been fitted to certain real life data sets. The asymptotic behaviour of maximum likelihood estimators of the parameters of the distribution are also studied by using simulated data sets. Keywords: Beta generalised inverse Weibull distribution, Failure rate, Generalised inverse Weibull distribution, Maximum likelihood estimation, Model selection, Percentile measures

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The Beta Generalized Inverse Weibull Distribution

Cited by 8 publications

References 14 publications

A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications

A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications

The Exponentiated Kumaraswamy InverseWeibull Distribution with Application in Survival Analysis

Inverse Kies distribution: Properties and applications

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