Modeling generalized statistical distributions of PM2.5 concentrations during the COVID-19 pandemic in Jakarta, Indonesia

Understanding the probabilistic or statistical behavior of air concentrations is necessary for the effective management of air pollution, such as PM2.5. Failure to consider the appropriateness of the model can lead to making inferences that are not supported by scientific evidence. The main focus of this article is to find the best statistical distribution in fitting PM2.5 concentrations in the periods of February–June 2018 and February–June 2019 (the periods without COVID-19) and in the period of February–June 2020 (the period with COVID-19) in Jakarta, Indonesia. This article considers making an assessment of the performance of both generalized distributions (e.g., generalized gamma, generalized extreme value, and generalized log-logistic [GLL]) and classical distributions (such as lognormal [LN], gamma, Weibull, log-logistic, and Gumbel) in modeling daily concentrations of PM2.5 in the period of February–June 2020, or the period during which the COVID-19 pandemic is present, in Jakarta. For comparison purposes, this study also analyzed PM2.5 concentrations in the periods of February–June 2018 and February–June 2019. The comparative evaluation of the models of each period of data uses graphical analyses and goodness-of-fit statistics. The results of applications indicate that the generalized distributions fit the data better than do the classical distributions. Particularly, compared with the classical distributions, including the LN model, the GLL distribution is the most appropriate model in fitting PM2.5 concentrations in the periods without and during the period with COVID-19 in Jakarta, Indonesia.

Generalized Beta-Exponential Weibull Distribution and its Applications

In this article, we investigate a distribution called the generalized beta-exponential Weibull distribution. Beta exponential x family of link function which is generated from family of generalized distributions is used in generating the new distribution. Its density and hazard functions have different shapes and contains special case of distributions that have been proposed in literature such as beta-Weibull, beta exponential, exponentiated-Weibull and exponentiated-exponential distribution. Various properties of the distribution were obtained namely; moments, generating function, Renyi entropy and quantile function. Estimation of model parameters through maximum likelihood estimation method and observed information matrix are derived. Thereafter, the proposed distribution is illustrated with applications to two different real data sets. Lastly, the distribution clearly shown that is better fitted to the two data sets than other distributions.

Modeling Life Time Data by Generalized Weibull-generalized Exponential Distribution

This paper convolutes two generalized distributions from the family of generated T - X distribution. The new distribution generated from these distributions is called the Generalized Weibull-generalized Exponential Distribution. The properties of the proposed distribution are derived. Method of maximum likelihood estimation is used to estimate the parameters of the distribution and the information matrix is obtained. Thereafter, the distribution is applied to a real life dataset of failure for the air conditioning system and the obtained results are compared with other existing distributions to illustrate the capability and flexibility of the new distribution.

Four generalized Weibull distributions: similar properties and applications

We derive a common linear representation for the densities of four generalizations of the two-parameter Weibull distribution in terms of Weibull densities. The four generalized Weibull distributions briefly studied are: the Marshall-Olkin-Weibull, beta-Weibull, gamma-Weibull and Kumaraswamy-Weibull distributions. We demonstrate that several mathematical properties of these generalizations can be obtained simultaneously from those of the Weibull properties. We present two applications to real data sets by comparing these generalized distributions. It is hoped that this paper encourage developments of further generalizations of the Weibull based on the same linear representation.