Inference Based on the Stochastic Expectation Maximization Algorithm in a Kumaraswamy Model with an Application to COVID-19 Cases in Chile (original) (raw)
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Extended Kumaraswamy Exponential Distribution with Application to COVID-19 Data set
Journal of Nepal Mathematical Society
There are many probability models describing the time related events data. In this study, the exponential distribution is modified by adding one more parameter to get more flexible probability model called Extended Kumaraswamy Exponential (EKwE) distribution using the New Kw-G family (NKwG) of distributions. We have studied some of the statistical characteristics of the model, such as its reliability function, hazard rate function, and quantile function. For testing the applicability of the model, a real data set based on COVID-19 data is taken. The Cramer-von Mises (CVM) approach, Least Square Estimation (LSE), and Maximum Likelihood Estimation (MLE) are used to estimate the model’s parameters. Validity of the model is checked by using P-P plot and Q-Q plot. Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC) and Hannan-Quinn Information Criterion (HQIC) are also used for model comparison. Goodness of fit of the pr...
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In this paper, we introduce a new flexible two-parameter unit interval univariate probability distribution called the "hybrid-Epanechnikov transformed Kumaraswamy distribution (HTKD)". The HTKD distribution, a flexible and robust version of the Kumaraswamy distribution, was created with the hybrid Epanechnikov kernel. We performed an in-depth analysis of its statistical characteristics and determined the parameters using the maximum likelihood estimation technique. The HTKD distribution's applicability was demonstrated using three datasets: the COVID-19 survival rate of Spain, the COVID-19 death rates of Canada, and the COVID-19 mortality rates of the UK. The HTKD distribution consistently offered the best fit when compared to other distributions, including the Beta, Kumaraswamy, BurrXII, and Weibull distributions, as seen by the lowest AIC and BIC values. These findings demonstrate the promise of the HTKD distribution as a flexible and useful tool for statistical analysis in epidemiological research. The uniformity of its performance across several datasets highlights its capacity to offer precise and dependable modelling of epidemiological data.
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Parameter Estimation for the Kumaraswamy Distribution Based on Hybrid Censoring
American Journal of Mathematical and Management Sciences, 2018
We consider estimation of unknown parameters of a two-parameter Kumaraswamy distribution with hybrid censored samples. We obtain maximum likelihood estimates using an expectation-maximization algorithm. Bayes estimates are derived under the squared error loss function using different approximation methods. In addition, an importance sampling technique is also discussed. Interval estimation is considered as well. We conduct a simulation study to compare the performance of different estimates, and based on this study, recommendations are made. A real data set and a simulated data set are analyzed for illustration purposes.
International Journal of ADVANCED AND APPLIED SCIENCES
This study aims to introduce an optimum model to assess the COVID-19 death rate in Saudi Arabia, Canada, Italy, and Mexico. A novel five-parameter lifetime distribution termed the Odd generalized exponential Kumaraswamy-inverse exponential distribution is presented by combining the Kumaraswamy-inverse exponential distribution with the odd generalized exponential generator. The theoretical features of the new distribution, as well as its reliability functions, moments, and order statistics are investigated. The odd generalized exponential Kumaraswamy-inverse exponential distribution is of special importance since its density has a variety of symmetric and asymmetric forms. Furthermore, the graphs of the hazard rate function exhibit various asymmetrical shapes such as decreasing, increasing, and upside-down bathtub shapes, and inverted J-shapes making The Odd generalized exponential Kumaraswamy-inverse exponential distribution suitable for modeling hazards behaviors more likely to be ...
Bayesian inference from the Kumaraswamy-Weibull distribution with applications to real data
International Journal of Contemporary Mathematical Sciences, 2016
This paper is concerned with the Bayesian analysis for the Kumaraswamy-Weibull (Kum-W) distribution under type II censored samples. Approximate Bayes estimates are computed using the Gibbs sampling procedure. This procedure generates samples from the posterior distributions. The approximate Bayes estimators are obtained under the assumptions of non-informative priors. Also, using Bayesian framework, the posterior density function, the predictive density for a single future response, i th ordered future response, and several future responses are derived under type II doubly censored samples. The predictive means, standard deviations, prediction intervals, and the shape characteristics for a single future response are determined. Applications to real data sets are utilized to illustrate the potentiality of the Bayesian analysis and the predictive results.