The quasi xgamma-geometric distribution with application in medicine

Sen, Subhradev; Afify, Ahmed Z.; Al-Mofleh, Hazem; Ahsanullah, Mohammad

doi:10.2298/fil1916291s

Cited by 23 publications

(19 citation statements)

References 26 publications

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“…The first set of data was studied by Lee and Wang [20], and it represents the remission times (in months) of a random sample of 128 bladder cancer patients. These data were analyzed by Sen et al [21], Afify et al [22], and Mansour et al [23]. The second set of data was studied by Kundu and Raqab [24], and it represents the gauge lengths of 20 mm of a sample of 74 observations.…”

Section: Applications In Medicine Engineering and Reliabilitymentioning

confidence: 99%

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

Afify

Mohamed

2020

Mathematics

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In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates, and right-skewed, left-skewed, symmetrical, and reversed-J shaped densities. Some mathematical properties of the proposed distribution are derived. The model parameters are estimated via eight frequentist estimation methods called, the maximum likelihood estimators, least squares and weighted least-squares estimators, maximum product of spacing estimators, Cramér-von Mises estimators, percentiles estimators, and Anderson-Darling and right-tail Anderson-Darling estimators. Extensive simulations are conducted to compare the performance of these estimation methods for small and large samples. Four practical data sets from the fields of medicine, engineering, and reliability are analyzed, proving the usefulness and flexibility of the proposed distribution.

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Section: Applications In Medicine Engineering and Reliabilitymentioning

confidence: 99%

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

Afify

Mohamed

2020

Mathematics

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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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“…In this section we analyze two different time-to-event data sets for illustrating the applicability of TPXG. For comparison purpose, besides TPXG, we consider five other two parameter lifetime distributions, viz., gamma distribution with shape and rate , weibull distribution with shape and scale , log-normal distribution with parameters and , two-parameter Lindley distribution (TPLD) with parameters alpha and (Shanker et al [7] and QXD with parameters and [3].…”

Section: Application With Real Life Data Illustrationmentioning

confidence: 99%

“…The xgamma distribution has several interesting structural and survival properties that made it useful in modeling time-to-event data sets. In another recent research paper, Sen and Chandra [3] introduced and studied different properties of a two-parameter extension or generalization of xgamma density, named as quasi xgamma distribution (QXD), and applied it in modeling bladder cancer survival data. QXD resembles closely with xgamma distribution in its density form and in other survival properties.…”

Section: Introductionmentioning

confidence: 99%

On Properties and Applications of a Two-Parameter Xgamma Distribution

Sen¹,

Chandra²,

Maiti³

2018

JSTA

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A B S T R A C TAn existing one-parameter probability distribution can be very well generalized by adding an extra parameter in it and, in turn, the two-parameter family of distributions, thus obtained, provides added flexibility in modeling real life data. In this article, we propose and study a two-parameter generalization of xgamma distribution [1] and utilize it in modeling time-to-event data sets. Along with the different structural and distributional properties of the proposed two-parameter xgamma distribution, we concentrate in studying useful survival and reliability properties, such as hazard rate, reversed hazard rate, stress-strength reliability etc. Two methods of estimation, viz. maximum likelihood and method of moments, are been suggested for estimating unknown parameters. Distributions of order statistics, stochastic order relationships are investigated for the proposed model. A Monte-Carlo simulation study is carried out to observe the trends in estimation process. Two real life time-to-event data sets are analyzed and the proposed model is compared with some other two-parameter lifetime models in the literature.This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). The TPXG along with its alternative form is introduced in section 2. The moments and related measures are studied in section 3. Incomplete moments are utilized in studying famous inequality curves and different entropy measures are studied in sections 4 and 5, respectively.

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The quasi xgamma-geometric distribution with application in medicine

Cited by 23 publications

References 26 publications

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

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

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

On Properties and Applications of a Two-Parameter Xgamma Distribution

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