Design of Multiple Dependent State Sampling Plan Application for COVID-19 Data Using Exponentiated Weibull Distribution

The proposed sampling plan in this article is referred to as multiple dependent state (MDS) sampling plans, for rejecting a lot based on properties of the current and preceding lot sampled. The median life of the product for the proposed sampling plan is assured based on a time-truncated life test, when a lifetime of the product follows exponentiated Weibull distribution (EWD). For the proposed plan, optimal parameters such as the number of preceding lots required for deciding whether to accept or reject the current lot, sample size, and rejection and acceptance numbers are obtained by the approach of two points on the operating characteristic curve (OC curve). Tables are constructed for various combinations of consumer and producer’s risks for various shape parameters. The proposed MDS sampling plan for EWD is demonstrated using the coronavirus (COVID-19) outbreak in China. The performance of the proposed sampling plan is compared with the existing single-sampling plan (SSP) when the quality of the product follows EWD.

Bayesian and Classical Inference for the Generalized Log-Logistic Distribution with Applications to Survival Data

The generalized log-logistic distribution is especially useful for modelling survival data with variable hazard rate shapes because it extends the log-logistic distribution by adding an extra parameter to the classical distribution, resulting in greater flexibility in analyzing and modelling various data types. We derive the fundamental mathematical and statistical properties of the proposed distribution in this paper. Many well-known lifetime special submodels are included in the proposed distribution, including the Weibull, log-logistic, exponential, and Burr XII distributions. The maximum likelihood method was used to estimate the unknown parameters of the proposed distribution, and a Monte Carlo simulation study was run to assess the estimators’ performance. This distribution is significant because it can model both monotone and nonmonotone hazard rate functions, which are quite common in survival and reliability data analysis. Furthermore, the proposed distribution’s flexibility and usefulness are demonstrated in a real-world data set and compared to its submodels, the Weibull, log-logistic, and Burr XII distributions, as well as other three-parameter parametric survival distributions, such as the exponentiated Weibull distribution, the three-parameter log-normal distribution, the three-parameter (or the shifted) log-logistic distribution, the three-parameter gamma distribution, and an exponentiated Weibull distribution. The proposed distribution is plausible, according to the goodness-of-fit, log-likelihood, and information criterion values. Finally, for the data set, Bayesian inference and Gibb’s sampling performance are used to compute the approximate Bayes estimates as well as the highest posterior density credible intervals, and the convergence diagnostic techniques based on Markov chain Monte Carlo techniques were used.

A universal Standardized Precipitation Index candidate distribution function for observations and simulations

The Standardized Precipitation Index (SPI) is a widely accepted drought index. Its calculation algorithm normalizes the index via a distribution function. Which distribution function to use is still disputed within the literature. This study illuminates that long-standing dispute and proposes a solution that ensures the normality of the index for all common accumulation periods in observations and simulations. We compare the normality of SPI time series derived with the gamma, Weibull, generalized gamma, and the exponentiated Weibull distribution. Our normality comparison is based on a complementary evaluation. Actual compared to theoretical occurrence probabilities of SPI categories evaluate the absolute performance of candidate distribution functions. Complementary, the Akaike information criterion evaluates candidate distribution functions relative to each other while analytically punishing complexity. SPI time series, spanning 1983–2013, are calculated from the Global Precipitation Climatology Project's monthly precipitation dataset, and seasonal precipitation hindcasts are from the Max Planck Institute Earth System Model. We evaluate these SPI time series over the global land area and for each continent individually during winter and summer. While focusing on regional performance disparities between observations and simulations that manifest in an accumulation period of 3 months, we additionally test the drawn conclusions for other common accumulation periods (1, 6, 9, and 12 months). Our results suggest that calculating SPI with the commonly used gamma distribution leads to deficiencies in the evaluation of ensemble simulations. Replacing it with the exponentiated Weibull distribution reduces the area of those regions where the index does not have any skill for precipitation obtained from ensemble simulations by more than one magnitude. The exponentiated Weibull distribution maximizes also the normality of SPI obtained from observational data and a single ensemble simulation. We demonstrate that calculating SPI with the exponentiated Weibull distribution delivers better results for each continent and every investigated accumulation period, irrespective of the heritage of the precipitation data. Therefore, we advocate the employment of the exponentiated Weibull distribution as the basis for SPI.

Estimation of the Parameters for the Exponentiated Weibull Distribution Based on Progressive Type-II Censoring Scheme

The main objective of the present study is to find the estimation of the two Exponentiated Weibull distribution parameters, based on progressive Type II censored samples. The maximum likelihood and Bayes estimators for the two shape parameters and the scale parameter of the exponentiated Weibull lifetime model were derived. Bayes estimators was obtained by using both the symmetric and asymmetric loss functions via squared error loss and linex loss functions This was done with respect to the conjugate priors for two shape parameters. We used an approximation based on the Lindley (Trabajos de Estadistca) method for obtaining Bayes estimates under these loss functions. The different proposed estimators have been compared through an extensive simulation studies. Bayes ratings also turned out to be better than MLE. Whatever the sample sizes are, we get the same results.

Statistical Learning of the Worst Regional Smog Extremes with Dynamic Conditional Modeling

This paper is concerned with the statistical learning of the extreme smog (PM 2.5 ) dynamics of a vast region in China. Differently from classical extreme value modeling approaches, this paper develops a dynamic model of conditional, exponentiated Weibull distribution modeling and analysis of regional smog extremes, particularly for the worst scenarios observed in each day. To gain higher modeling efficiency, weather factors will be introduced in an enhanced model. The proposed model and the enhanced model are illustrated with temporal/spatial maxima of hourly PM 2.5 observations each day from smog monitoring stations located in the Beijing–Tianjin–Hebei geographical region between 2014 and 2019. The proposed model performs more precisely on fittings compared with other previous models dealing with maxima with autoregressive parameter dynamics, and provides relatively accurate prediction as well. The findings enhance the understanding of how severe extreme smog scenarios can be and provide useful information for the central/local government to conduct coordinated PM 2.5 control and treatment. For completeness, probabilistic properties of the proposed model were investigated. Statistical estimation based on the conditional maximum likelihood principle is established. To demonstrate the estimation and inference efficiency of studies, extensive simulations were also implemented.