An extended approach for the generalized powered uniform distribution (original) (raw)
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In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, “unimodal”, or “bathtub-shaped“ hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently m...
Journal of Probability and Statistical Science
Attempts have been made to define new families of distributions that provide more flexibility for modelling data that is skewed in nature. In this work, we propose a new family of distributions called Marshall-Olkin-odd power generalized Weibull (MO-OPGW-G) distribution based on the generator pioneered by Marshall and Olkin [20]. This new family of distributions allows for a flexible fit to real data from several fields, such as engineering, hydrology and survival analysis. The mathematical and statistical properties of these distributions are studied and its model parameters are obtained through the maximum likelihood method. We finally demonstrate the effectiveness of these models via simulation experiments and applications to COVID-19 daily deaths data sets.
IJSRED, 2023
This paper major goal is to create a model that may be used to model Italy’s Covid-19 Mortality rate. The Alpha Power Exponentiated Inverse Exponential distribution, often known as the APEIEx distribution, is employed in this situation with two shapes and one or more scale parameters. In this work, significant statistical features including the Survival function, Hazard function, Quantile function, the Middle value (Median), the Lower (1st) quantile, the Upper (3rd) quantile, the r th Moment, the Moment generating function, and the order statistics are investigated. With the aid of the BFGS method, the parameters of the proposed distribution are determined using maximum likelihood estimation. When compared to other distributions employed in this investigation, the proposed distribution clearly offers a better fit for the Italy’s Covid-19 Mortality rates data. This demonstrates the flexibility and adaptability of the APEIEx distribution for the Covid-19 Mortality rates in Italy
Modeling COVID-19 Data with a Novel Extended Exponentiated Class of Distributions
Journal of Mathematics
The COVID-19 epidemic has affected every aspect of daily life since December 2019 and caused massive damage to the world. The coronavirus epidemic has affected more than 150 countries around the world. Many researchers have tried to develop a statistical model which can be utilized to analyze the behavior of the COVID-19 data. This article contributes to the field of probability theory by introducing a novel family of distributions, named the novel extended exponentiated class of distributions. Explicit expressions for numerous mathematical characterizations of the proposed family have been obtained with special concentration on a three-parameter submodel of the new class of distributions, named the new extended exponentiated Weibull distribution. The unknown model parameter estimates are obtained via the maximum likelihood estimation method. To assess the performance of these estimates, a comprehensive simulation study is conducted. Three different sets of COVID-19 data are used to...
Exponentiated Generalized Exponential Geometric Distribution: Model, Properties and Applications
Interdisciplinary Journal of Management and Social Sciences
In this article, a new distribution called Exponentiated Generalized Exponential Geometric Distribution is formulated. We have derived some important mathematical properties like hazard function, probability density function, survival function, quantiles, the measures of skewness based on quartiles and coefficient of kurtosis based on octiles. To estimate the parameters of the new distribution, we have applied the three commonly used estimation methods namely maximum likelihood estimation (MLE), least-square (LSE) method and Cramer-Von-Mises (CVM) method. We have used R programming as well as analytical methods for data analysis. For model validation, we have used different information criteria as Akaike’s information criteria, and Bayesian information criteria (BIC) etc. For the assessment of potentiality of the new distribution, we have considered a real dataset and the goodness-of-fit attained by proposed distribution is compared with some competing distributions. It is found tha...
Generalized Exponential Power Distribution with Application to Complete and Censored Data
Asian Journal of Probability and Statistics, 2021
The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.