Maximum Product Spacing Estimation of Weibull Distribution Under Adaptive Type-II Progressive Censoring Schemes

Computational Intelligence and Neuroscience

Gemeay

et al. 2021

In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Fréchet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient’s survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov–Smirnov (KS) algorithm for fitting Type-I censored data.

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Section: Point Estimation Methodsmentioning

confidence: 99%

Statistical Inference under Censored Data for the New Exponential-X Fréchet Distribution: Simulation and Application to Leukemia Data

Alzeley

Computational Intelligence and Neuroscience

Gemeay

et al. 2021

“…In future studies, we intend to make a new extension bivariate modified Kies inverted Topp-Leone based on copula such as and Muhammed and Almetwally [18], Almetwally and Muhammed [19], El-Morshedy et al [20], and Kim et al [21]. We intend to discuss a new application based on a censored sample for MKITL distribution see for more reading, Almetwally et al [22] and Aslam et al [23].…”

Section: Introductionmentioning

confidence: 99%

A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Alharbi

Alnagar

et al. 2021

Axioms

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

“…We plan to make a new extension bivariate OWITL based on copula in future studies, such as done in Almetwally et al [ 34 ], Muhammed and Almetwally [ 35 ] and Kim et al [ 36 ]. We plan to discuss a new application for the OWITL distribution quest based on a censored sample such as done in Almetwally et al [ 37 ] and Aslam et al [ 38 ].…”

Section: Introductionmentioning

confidence: 99%

The Odd Weibull Inverse Topp–Leone Distribution with Applications to COVID-19 Data

2021

Ann. Data. Sci.

This paper aims at defining an optimal statistical model for the COVID-19 distribution in the United Kingdom, and Canada. A combining the inverted Topp–Leone distribution and the odd Weibull family introduces a new lifetime distribution with a three-parameter to formulate the odd Weibull inverted Topp–Leone (OWITL) distribution. As a simple linear representation, hazard rate function, and moment function, this new distribution has several nice properties. To estimate the unknown parameters of OWITL distribution, maximum likelihood, least-square, weighted least-squares, maximum product spacing, Cramér–von Mises estimators, and Anderson–Darling estimation methods are used. To evaluate the use of estimation techniques, a numerical outcome of the Monte Carlo simulation is obtained.