In this research, we present an alternative statistical framework for analyzing cancer data, concentrating on the limits of existing lifetime failure models. By incorporating a New Alpha-power function distribution (N...
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In this research, we present an alternative statistical framework for analyzing cancer data, concentrating on the limits of existing lifetime failure models. By incorporating a New Alpha-power function distribution (NAPFD) into the larger Alpha-power Generated (APG) class, our approach outperforms standard models such as lognormal, Weibull, and generalized extreme value distributions in handling complex failure rate data patterns found in medical datasets. The NAPFD displays superior model fit and predicted accuracy in a careful comparison examination of five separate medical datasets, as evidenced by extensive goodness-of-fit criteria. Furthermore, we investigate the usefulness of numerous classical estimate strategies using simulation experiments, evaluating their performance using parameters such as absolute bias, mean square error, and mean relative error.
In practice,the control charts for monitoring of process mean are based on the normality *** the performance of the control charts is seriously affected if the process of quality characteristics departs from *** such ...
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In practice,the control charts for monitoring of process mean are based on the normality *** the performance of the control charts is seriously affected if the process of quality characteristics departs from *** such situations,we have modified the already existing control charts such as Shewhart control chart,exponentially weighted moving average(EWMA)control chart and hybrid exponentially weighted moving average(HEWMA)control chart by assuming that the distribution of underlying process follows power function distribution(PFD).By considering the situation that the parameters of PFD are unknown,we estimate them by using three classical estimation methods,i.e.,percentile estimator(P.E),maximum likelihood estimator(MLE)and modified maximum likelihood estimator(MMLE).We construct Shewhart,EWMA and HEWMA control charts based on P.E,MLE and *** have compared all these control charts using Monte Carlo simulation studies and concluded that HEWMA control chart under MLE is more sensitive to detect an early shift in the shape parameter when the distribution of the underlying process follows power function distribution.
In this article we introduce and study a new four-parameter distribution, called the odd generalized exponential power function distribution. The proposed model is a particular case from the odd generalized exponentia...
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In this article we introduce and study a new four-parameter distribution, called the odd generalized exponential power function distribution. The proposed model is a particular case from the odd generalized exponential family. Expressions for the moments, probability weighted moments, quantile function, Bonferroni and Lorenz curves, Renyi entropy and order statistics are obtained. The model parameters are estimated via the maximum likelihood and percentiles methods of estimation. A simulation study is carried out to evaluate and compare the performance of estimates in terms of their biases, standard errors and mean square errors. Eventually, the practical importance and flexibility of the proposed distribution in modelling real data application is checked. It can be concluded that the new distribution works better than some other known distributions.
In order to improve the already existing models that are used extensively in bio sciences and applied sciences research, a new class of Weighted power function distribution (WPFD) has been proposed with its various pr...
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In order to improve the already existing models that are used extensively in bio sciences and applied sciences research, a new class of Weighted power function distribution (WPFD) has been proposed with its various properties and different modifications to be more applicable in real life. We have provided the mathematical derivations for the new distribution. The aim of the study is to increase the application of the power function distribution. The main feature of the proposed distribution is that there is no induction of parameters as compared to the other generalisation of the distributions, which are complex, having many parameters. We have used R programming to estimate the parameters of the new class of WPFD using Maximum Likelihood Method (MLM), Percentile Estimators (PE) and their modified estimators. After analysing the data, we conclude that the proposed model WPFD performs better in the data sets while compared to different competitor models.
powerfunction is amougst the most suitable probability models for survival or failure times analysis, particularly of electronic components and product reliability. The article proposes some new modified moment estim...
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powerfunction is amougst the most suitable probability models for survival or failure times analysis, particularly of electronic components and product reliability. The article proposes some new modified moment estimators for parameter estimation of the power function distribution. The proposed estimators are based on some non-conventional descriptive measures like harmonic mean, quartile deviation, Shannon entropy and Gini index. The performance of the proposed estimators is compared with the traditional moment and existing modified moment estimators. Performance is assessed through the Monte Carlo simulation and three real-life data sets representing failure and survival times of components and infected animals, respectively. Some common accuracy measures are used as performance indicators. From both, Monte Carlo simulation and all real-life applications, the results show better performance of proposed modified moment estimators based on the Gini index and harmonic mean. Hence, the use of these modified estimators is recommended for parameter estimation of the power function distribution.
In this study, we have focused to propose a flexible model that demonstrates increasing, decreasing and upside-down bathtub-shaped density and failure rate functions. The proposed model refers to as the exponentiated ...
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In this study, we have focused to propose a flexible model that demonstrates increasing, decreasing and upside-down bathtub-shaped density and failure rate functions. The proposed model refers to as the exponentiated powerfunction (EPF) distribution. Some mathematical and reliability measures are developed and derived. We develop explicit expressions for the moments, quantile function and order statistics. Some shapes of the density and the reliability functions are sketched out and discussed. We suggest the method to estimate the unknown parameters of EPF by the maximum likelihood estimation. Two suitable lifetime datasets from engineering sector are used to explore the dominance of the EPF distribution. (c) 2020 The Authors. Published by Atlantis Press SARL.
Letbe a random sample from a population with probability density function (p.d.f.) f(x), (x>0) and letbe the associated order statistics, A necessary and sufficient condition (NASC) based on the statistics Xr,n/Xs,...
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Letbe a random sample from a population with probability density function (p.d.f.) f(x), (x>0) and letbe the associated order statistics, A necessary and sufficient condition (NASC) based on the statistics Xr,n/Xs,n(1≤r≤s≤n) and Xs,nthat a p.d.f.f(x), x>0 will he the density of power function distribution is given.
This paper, introduces the power function distribution considers some of the important descriptive statistics that provide an accurate measures of central tendency and dispersion based on moment-generating functions a...
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This paper, introduces the power function distribution considers some of the important descriptive statistics that provide an accurate measures of central tendency and dispersion based on moment-generating functions and provided some special cases related to the power function distribution.
Abstract: In this article, we introduce an extension referred to as the exponentiated Weibull power function distribution based on the exponentiated Weibull-G family of distributions. The proposed model serves as an e...
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Abstract: In this article, we introduce an extension referred to as the exponentiated Weibull power function distribution based on the exponentiated Weibull-G family of distributions. The proposed model serves as an extension of the two-parameter power function distribution as well as a generalization to the Weibull powerfunction presented by Tahir et al. (2016 a). Various mathematical properties of the subject distribution are studied. General explicit expressions for the quantile function, expansion of density and distributionfunctions, moments, generating function, incomplete moments, conditional moments, residual life function, mean deviation, inequality measures, Rényi and q - entropies, probability weighted moments and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. Finally, the practical importance of the proposed distribution is examined through three real data sets. It has been concluded that the new distribution works better than other competing models.
By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey, 2004 which we called the Transform...
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By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey, 2004 which we called the Transformed powerfunction (TPF) distribution and based on an alpha-power transformation method due to Mahdavi and Kundu, (2017) we generalized the TPF distribution as the alpha-power Transformed Transformed powerfunction (alpha PTTPF) distribution. Some of the properties of the alpha PTTPF distribution are given, and we approached the parameter estimation by three methods, namely: maximum likelihood, ordinary least-squares, and weighted least-squares, but after comparing the results from a simulation study, we settled for the maximum likelihood. The new distribution is suitable for modeling data with either decreasing or upside-down bathtub hazard rates. Three real data-sets are used to demonstrate the usefulness of the new model.
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