7 research outputs found
Survival analysis based on an enhanced Rayleigh-inverted Weibull model
No full textThis study proposes a two-parameter survival model based on the Kavya-Manoharan transformation family and the Rayleigh-inverted Weibull distribution, the so-called Kavya-Manoharan-Rayleigh inverted Weibull distribution (KMRIWD). Various reliability measures and statistical properties of this distribution are analyzed. The parameters of the distribution are estimated using the maximum likelihood method and different sampling techniques. Using Monte Carlo simulations, the performance of the estimators is evaluated and compared. Finally, the model and numerous competitors are compared using real data sets, and it is shown that the KMRIWD has a better fit than all the competitors
Statistical Inference for Heavy-Tailed Burr X Distribution with Applications
No full textIn this article, we present a new distribution, the so-called heavy-tailed Burr X (HTBX) distribution. It comes from the newly discovered heavy-tailed (HT) family of distributions. A notable feature is that the associated probability density function can have a right-skewed distribution that approximates symmetry, unimodality, and decreasing values, which makes it well suited for modeling various datasets. The mathematical properties of the new distribution are obtained by calculating the quantile function, ordinary moments, incomplete moments, moment generating function, conditional moment, mean deviation, Bonferroni curve, and Lorenz curve. Extensive simulation was performed to investigate the estimation of the model parameters using many established approaches, including maximum likelihood estimation, least squares estimation, weighted least squares estimation, Cramer–von Mises estimation, Anderson–Darling estimation, maximum product of spacing estimation, and percentile estimation. The simulation results showed the computational efficiency of these strategies and showed that the maximum likelihood strategy of estimation is the best strategy. The utility and importance of the newly proposed model are demonstrated by analyzing three real datasets. The HTBX distribution is compared to several well-known extensions of the Burr distribution such as exponentiated Kavya-Manoharan Burr X, Kavya-Manoharan Burr X, Burr X, Kumaraswamy Rayleigh, Kumaraswamy Burr III, exponentiated Burr III, Burr III, Kumaraswamy Burr-II, Rayleigh, and HT Rayleigh models by using different measures. The numerical results showed that the HTBX model fit the data better than the other competitive models
The EX-Lindley distribution with applications to renewable energy sources data
No full textThis study introduces a novel extension of the X-Lindley model, called the EX-Lindley model. The EX-Lindley model is a mixture model that combines the characteristics of the gamma model with the weighted Lindley model. The EX-Lindley model is analyzed to determine various statistical properties, including ordinary moments, inverse moments, moment generating function, incomplete moments, conditional moments, mean deviation, Lorenz, mean residual life, mean inactivity time, order statistics, and extropy. The maximum likelihood method is employed to estimate model parameters using complete data. Moreover, the simulation study is used to compare and evaluate the attributes of the estimations for this generalized model. Finally, two examples of datasets on renewable energy sources are utilized to show the importance of the new model compared to some well-known statistical models
DUS Topp–Leone-G Family of Distributions: Baseline Extension, Properties, Estimation, Simulation and Useful Applications
No full textThis study introduces the DUS Topp–Leone family of distributions, a novel extension of the Topp–Leone distribution enhanced by the DUS transformer. We derive the cumulative distribution function (CDF) and probability density function (PDF), demonstrating the distribution’s flexibility in modeling various lifetime phenomena. The DUS-TL exponential distribution was studied as a sub-model, with analytical and graphical evidence revealing that it exhibits a unique unimodal shape, along with fat-tail characteristics, making it suitable for time-to-event data analysis. We evaluate parameter estimation methods, revealing that non-Bayesian approaches, particularly Maximum Likelihood and Least Squares, outperform Bayesian techniques in terms of bias and root mean square error. Additionally, the distribution effectively models datasets with varying skewness and kurtosis values, as illustrated by its application to total factor productivity data across African countries and the mortality rate of people who injected drugs. Overall, the DUS Topp–Leone family represents a significant advancement in statistical modeling, offering robust tools for researchers in diverse fields
A flexible statistical distribution for capturing complex patterns in industrial data
No full textThe effective modeling of real-world data requires flexible statistical distributions to accurately capture complex patterns. For that purpose, this paper introduces an extension of the XLindley distribution, specifically designed for modeling textile data. The suggested Marshall-Olkin transmuted XLindley distribution (MOTXLD) has additional shape and transmuted parameters, which considerably influence its skewness, kurtosis, and tail behavior. The MOTXLD is versatile and can have right-skewed, uni-modal, or reversed-J-shaped density curves. A comprehensive statistical analysis of the MOTXLD is conducted, including the derivation of key properties. To estimate the model parameters, both frequentist and Bayesian techniques are implemented. The bootstrap approach, the normal approximation method, and Bayesian credible intervals are some of the techniques employed to build confidence intervals. A simulation study is conducted to assess the efficiency of the estimated parameters. According to the outcomes of this study, Bayesian estimates often perform better than frequentist estimates. Bayesian credible intervals generally show a higher coverage probability compared to confidence intervals based on maximum likelihood estimation, implying more reliable interval estimates. The adaptability of the proposed distribution is demonstrated using real datasets from the textile industry sector, highlighting its potential for effective modeling in this domain
Sine power Burr X distribution with estimation and applications in physics and other fields
No full textThis article aims to introduce a new three-parameter lifetime distribution called sine power Burr X (SPB-X) distribution. The proposed distribution is obtained by the sine-G class of distributions and the power Burr X distribution. Various properties of the proposed distribution, including explicit expressions for the quantile function, Bowley skewness, Moors kurtosis, ordinary moments, generating function, incomplete and conditional moments, and some numerical and graphical illustrations, are provided. Some various significant reliability metrics for the SPB-X model, including common reliability functions, mean residual life function, mean waiting time function, residual moment, and reversed residual life. Several essential risk measures for the SPB-X distribution. These risk measures include the value at risk, the expected shortfall, the tail value at risk, the tail variance, and the tail variance premium. Four estimation methods were employed to estimate the model’s parameters such as maximum likelihood, least squares, maximum product spacing, and Bayesian. A simulation study is conducted to assess the performance of the estimation methods. Finally, five real data are considered to analyze the usefulness and flexibility of the proposed model
