A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Afify, Ahmed Z.; Mohamed, Osama G.

doi:10.3390/math8010135

Cited by 42 publications

(32 citation statements)

References 26 publications

(29 reference statements)

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“…In this section, we consider nine methods of estimation to estimate the unknown parameters of the APE distribution. The used estimation methods are (1)…”

Section: Methods Of Estimationmentioning

confidence: 99%

Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

Nassar

Afify

Shakhatreh

2020

Pak.j.stat.oper.res.

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This paper addresses the estimation of the unknown parameters of the alphapower exponential distribution (Mahdavi and Kundu, 2017) using nine frequentist estimation methods. We discuss the nite sample properties of the parameterestimates of the alpha power exponential distribution via Monte Carlo simulations. The potentiality of the distribution is analyzed by means of two real datasets from the elds of engineering and medicine. Finally, we use the maximumlikelihood method to derive the estimates of the distribution parameters undercompeting risks data and analyze one real data set.

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“…In this section, we consider nine methods of estimation to estimate the unknown parameters of the APE distribution. The used estimation methods are (1)…”

Section: Methods Of Estimationmentioning

confidence: 99%

Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

Nassar

Afify

Shakhatreh

2020

Pak.j.stat.oper.res.

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“…The data are available at: https: //catalog.data.gov/dataset/unemployment-insurance-data-july-2008-to-april-2013. We compare the goodness-of-fit results and some discrimination measures of the proposed distribution with some other well-known competing distributions, including the APE [20], ExE [21], beta exponential (BE) [32], E, extended odd Weibull exponential (EOWE) [33], exponentiated Weibull (ExW) [34], Weibull (W), transmuted generalized exponential (TGE) [35], Marshall-Olkin exponential (MOE) [36], generalized transmuted exponential (GTE) [37], transmuted exponentiated generalized exponential (TExGE) [38], complementary geometric transmuted exponential (CGTE) [39], gamma (G), Harris extended exponential (HEE) [40], and transmuted exponential (TE) [41] distributions.…”

Section: Modeling Insurance Datamentioning

confidence: 99%

The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data

2020

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Modeling insurance data using heavy-tailed distributions is of great interest for actuaries. Probability distributions present a description of risk exposure, where the level of exposure to the risk can be determined by “key risk indicators” that usually are functions of the model. Actuaries and risk managers often use such key risk indicators to determine the degree to which their companies are subject to particular aspects of risk, which arise from changes in underlying variables such as prices of equity, interest rates, or exchange rates. The present study proposes a new heavy-tailed exponential distribution that accommodates bathtub, upside-down bathtub, decreasing, decreasing-constant, and increasing hazard rates. Actuarial measures including value at risk, tail value at risk, tail variance, and tail variance premium are derived. A computational study for these actuarial measures is conducted, proving that the proposed distribution has a heavier tail as compared with the alpha power exponential, exponentiated exponential, and exponential distributions. We adopt six estimation approaches for estimating its parameters, and assess the performance of these estimators via Monte Carlo simulations. Finally, an actuarial real data set is analyzed, proving that the proposed model can be used effectively to model insurance data as compared with fifteen competing distributions.

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“…For example, [32] used the Weibull and MOW distributions to model the survival times of the cancer patients. These data were analyzed by [33] and [34].…”

Section: A Real Life Application From Bio-medical Sciencesmentioning

confidence: 99%

Type-I heavy tailed family with applications in medicine, engineering and insurance

et al. 2020

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In the present study, a new class of heavy tailed distributions using the T-X family approach is introduced. The proposed family is called type-I heavy tailed family. A special model of the proposed class, named Type-I Heavy Tailed Weibull (TI-HTW) model is studied in detail. We adopt the approach of maximum likelihood estimation for estimating its parameters, and assess the maximum likelihood performance based on biases and mean squared errors via a Monte Carlo simulation framework. Actuarial quantities such as value at risk and tail value at risk are derived. A simulation study for these actuarial measures is conducted, proving that the proposed TI-HTW is a heavy-tailed model. Finally, we provide a comparative study to illustrate the proposed method by analyzing three real data sets from different disciplines such as reliability engineering, bio-medical and financial sciences. The analytical results of the new TI-HTW model are compared with the Weibull and some other non-nested distributions. The Baysesian analysis is discussed to measure the model complexity based on the deviance information criterion.

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A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Cited by 42 publications

References 26 publications

Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data

Type-I heavy tailed family with applications in medicine, engineering and insurance

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