A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension

Statistical analysis of air quality dataset of Kathmandu, Nepal, with a New Extended Kumaraswamy Exponential Distribution

This paper aims to create a new probability distribution and conducts statistical analysis on air quality dataset from Kathmandu. Using this innovative distribution, we have studied the ground reality of air quality conditions of Kathmandu, Nepal. In our research, we have developed a new probability distribution known as the New Extended Kumaraswamy Exponential Distribution by introducing an additional shape parameter to the Extended Kumaraswamy Exponential (EKwE) Distribution. Statistical characteristics such as cumulative distribution function, probability density function, hazard function, reversed hazard function, skewness, kurtosis, survival function, and hazard rate function are studied. The suggested model is non-normal and positively skewed with increasing and inverted bathtub-shaped hazard rate curves. To assess the model's suitability, we utilized a real dataset comprising air quality data from Kathmandu, Nepal, during the year 2021. Study shows that the air quality data exhibit an increasing failure rate, but the P2.5, P10, and total suspended particle concentrations exhibited its lowest levels during the monsoon season and its highest levels during the winter season. Parameters of the model are estimated by using the least square estimation (LSE), maximum likelihood estimation (MLE), and Cramér-von Mises (CVM) approach for P10 at Ratnapark Station, Kathmandu. To assess the model's validity, P-P plots and Q-Q plots are employed. Model comparisons are carried out using Akaike Information Criterion (AIC), Corrected Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC), and Hannan-Quinn Information Criterion (HQIC). Furthermore, the goodness of fit of the proposed model is evaluated using test statistics such as Anderson-Darling (A2) test, Cramér-von Mises (CVM) test, and the Kolmogorov-Smirnov (KS) test along with their respective p-values. From the findings, we have found that the air quality status of Kathmandu, Nepal, was found to be poor. Proposed distribution provides a better fit with greater flexibility for forecasting air quality data and conducting reliability data analyses. Dataset is analyzed and visualized using R programming.

A new Topp-Leone Kumaraswamy Marshall-Olkin generated family of distributions with applications

We aim in this paper to propose a novel class of distributions that was created by merging the Topp-Leone distribution and the Generated families of Kumaraswamy and Marshall-Olkin. Its cumulative distribution function characterizes it and includes rational and polynomial functions. In particular, the following desirable properties of the new family are presented: Shannon entropy, order statistics, the quantile power series, and several associated measures and functions. Then, using a specific family member identified before, we create a parametric statistical model with the basic distribution being the inverse exponential distribution. Finally, a thorough investigation has been made to implement this new distribution with three data sets: the glass fibers data set, the glass Alumina data set and the hailing times data set. In comparison to six prominent competitors, the new model performs favorably on all statistical tests and criteria that were examined.

On the implementation of a new version of the Weibull distribution and machine learning approach to model the COVID-19 data

Statistical methodologies have broader applications in almost every sector of life including education, hydrology, reliability, management, and healthcare sciences. Among these sectors, statistical modeling and predicting data in the healthcare sector is very crucial. In this paper, we introduce a new method, namely, a new extended exponential family to update the distributional flexibility of the existing models. Based on this approach, a new version of the Weibull model, namely, a new extended exponential Weibull model is introduced. The applicability of the new extended exponential Weibull model is shown by considering two data sets taken from the health sciences. The first data set represents the mortality rate of the patients infected by the coronavirus disease 2019 (COVID-19) in Mexico. Whereas, the second set represents the mortality rate of COVID-19 patients in Holland. Utilizing the same data sets, we carry out forecasting using three machine learning (ML) methods including support vector regression (SVR), random forest (RF), and neural network autoregression (NNAR). To assess their forecasting performances, two statistical accuracy measures, namely, root mean square error (RMSE) and mean absolute error (MAE) are considered. Based on our findings, it is observed that the RF algorithm is very effective in predicting the death rate of the COVID-19 data in Mexico. Whereas, for the second data, the SVR performs better as compared to the other methods.

A New Flexible Univariate and Bivariate Family of Distributions for Unit Interval (0, 1)

We propose a new generator for unit interval which is used to establish univariate and bivariate families of distributions. The univariate family can serve as an alternate to the Kumaraswamy-G univariate family proposed earlier by Cordeiro and de-Castro in 2011. Further, the new generator can also be used to develop more alternate univariate and bivariate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for support (0, 1). Some structural properties of the univariate family are derived and the estimation of parameters is dealt. The properties of a special model of this new univariate family called a New Kumaraswamy-Weibull (NKwW) distribution are obtained and parameter estimation is considered. A Monte Carlo simulation is reported to assess NKwW model parameters. The bivariate extension of the family is proposed and the estimation of parameters is described. The simulation study is also conducted for bivariate model. Finally, the usefulness of the univariate NKwW model is illustrated empirically by means of three real-life data sets on Air Conditioned Failures, Flood and Breaking Strength of Fibers, and one real-life data on UEFA Champion’s League for bivariate model.

Gompertz Ampadu Class of Distributions: Properties and Applications

This paper introduces a new generator family of distributions called the Gompertz Ampadu-G family. Based on the generator, the Lomax distribution was modified into Gompertz Ampadu Lomax. The new distribution has a flexible hazard rate function that has upside-down and bathtub shapes, including increasing and decreasing hazard rate functions. The distribution comes with some desirable statistical properties. The distribution is applied to real-life data. Parameter estimates and test statistics show a better fit for the competitive models.

A New Flexible Family of Continuous Distributions: The Additive Odd-G Family

This paper introduces a new family of distributions based on the additive model structure. Three submodels of the proposed family are studied in detail. Two simulation studies were performed to discuss the maximum likelihood estimators of the model parameters. The log location-scale regression model based on a new generalization of the Weibull distribution is introduced. Three datasets were used to show the importance of the proposed family. Based on the empirical results, we concluded that the proposed family is quite competitive compared to other models.

A Flexible Extension to an Extreme Distribution

The aim of this paper is not only to propose a new extreme distribution, but also to show that the new extreme model can be used as an alternative to well-known distributions in the literature to model various kinds of datasets in different fields. Several of its statistical properties are explored. It is found that the new extreme model can be utilized for modeling both asymmetric and symmetric datasets, which suffer from over- and under-dispersed phenomena. Moreover, the hazard rate function can be constant, increasing, increasing–constant, or unimodal shaped. The maximum likelihood method is used to estimate the model parameters based on complete and censored samples. Finally, a significant amount of simulations was conducted along with real data applications to illustrate the use of the new extreme distribution.

Bayesian and Frequentist Inferences on a Type I Half-Logistic Odd Weibull Generator with Applications in Engineering

In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.

A new one-parameter lifetime distribution and its regression model with applications

Lifetime distributions are an important statistical tools to model the different characteristics of lifetime data sets. The statistical literature contains very sophisticated distributions to analyze these kind of data sets. However, these distributions have many parameters which cause a problem in estimation step. To open a new opportunity in modeling these kind of data sets, we propose a new extension of half-logistic distribution by using the odd Lindley-G family of distributions. The proposed distribution has only one parameter and simple mathematical forms. The statistical properties of the proposed distributions, including complete and incomplete moments, quantile function and Rényi entropy, are studied in detail. The unknown model parameter is estimated by using the different estimation methods, namely, maximum likelihood, least square, weighted least square and Cramer-von Mises. The extensive simulation study is given to compare the finite sample performance of parameter estimation methods based on the complete and progressive Type-II censored samples. Additionally, a new log-location-scale regression model is introduced based on a new distribution. The residual analysis of a new regression model is given comprehensively. To convince the readers in favour of the proposed distribution, three real data sets are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other extensions of half-logistic distribution.

A New Family of Continuous Probability Distributions

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of "Farlie-Gumbel-Morgenstern copula", "the modified Farlie-Gumbel-Morgenstern copula", "the Clayton copula", and "the Renyi's entropy copula" are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.