Joseph Thomas

Bio: Joseph Thomas is an academic researcher. The author has contributed to research in topics: Exponential distribution & Quantile. The author has an hindex of 2, co-authored 2 publications receiving 16 citations.

Theoretical Analysis of the Weibull Alpha Power Inverted Exponential Distribution: Properties and Applications

Abstract: This article proposed a Weibull-Alpha Power Inverted Exponential (WAPIE) distribution for lifetime processes. Statistical properties of this distribution such as survival, hazard, reversed hazard, cumulative, odd functions, kurtosis, quantiles, skewness, order statistics and the entropies were derived. Parameters of this family of distribution were also obtained by maximum likelihood method. The behaviour of the estimators was studied through simulation. The behavior of the new developed distribution was further examined through real life data. The WAPIE distribution competes favourably well with other distributions.

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

Abstract: 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.

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

Abstract: 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, Cramer–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.

The Alpha Power Gompertz Distribution: Characterization, Properties, and Applications

Abstract: A new three-parameter model called the Alpha power Gompertz is derived, studied and proposed for modeling lifetime Poisson processes. The advantage of the new model is that, it has left skew, decreasing, unimodal density with a bathtub shaped hazard rate function. The statistical structural properties of the proposed model such as probability weighted moments, moments, order statistics, entropies, hazard rate, survival, quantile, odd, reversed hazard, moment generating and cumulative functions are investigated. The new proposed model is expressed as a linear mixture of Gompertz densities. The parameters of the proposed model were obtained using maximum likelihood method. The behaviour of the new density is examined through simulation. The proposed model was applied to two real-life data sets to demonstrate its flexibility. The new density proposes provides a better fit when compared with other existing models and can serve as an alternative model in the literature.

The Alpha Power Marshall-Olkin-G Distribution: Properties, and Applications

Abstract: In this article, a new family of distribution called the alpha power Marshall-Olkin-G (APMO-G) family of distributions was proposed. The new family of distribution provides a better fit for continuous distributions for lifetime processes. The proposed family of distributions extends the existing alpha power transformed family of distributions by an additional parameter. A comprehensive reliability structural properties were derived. The moments, order statistics, hazard rate, and quantile functions, were also examined. The parameters of the proposed APMO-G model were obtained by the maximum likelihood method. Monte Carlo simulation was used to access the performance of the estimators. The goodness-of-fit test statistics were examined by means of two real-life data sets to demonstrate empirical flexibility. The results show that the APMO-G density provides a better fit when compared with other existing models and can serve as a better alternative model in the literature.

The transmuted alpha power-G family of distributions

Abstract: This article proposes a new class of models called the transmuted alpha power-G (TAPO-G) family of distribution for modeling lifetime processes. This class of model extends the well-known existing ...