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In this study, a new one-parameter discrete probability distribution is introduced for overdispersed count data based on a combining approach. The important statistical properties can be expressed in closed forms including factorial moments, moment generating function, dispersion index, coefficient of variation, coefficient of skewness, coefficient of kurtosis, value at risk, and tail value at risk. Moreover, four classical parameter estimation methods have been discussed for this new distribution. A simulation study was conducted to evaluate the performance of different estimators based on the biases, mean related-errors, and mean square errors of the estimators. In the end, real data sets from different fields are analyzed to verify the usefulness of the new probability mass function over some notable discrete distributions. It is manifested that the new discrete probability distribution provides an adequate fit than these distributions.

The Weibull distribution has always been important in numerous areas because of its vast variety of applications. In this paper, basic properties of the neutrosophic Weibull distribution are derived. The effect of indeterminacy is studied on parameter estimation. The application of the neutrosophic Weibull distribution will be discussed with the help of two real-life datasets. From the analysis, it can be seen that the neutrosophic Weibull model is adequate, reasonable, and effective to apply in an uncertain environment.

The most suitable source of energy for human use is wind energy, which is competitive and supports the energy demand of a large population. In this study, we introduced a new probability distribution for the analysis of wind speed data. The newly developed distribution is known as “New Alpha power transformed power Lindley”. Some mathematical properties of the proposed distribution were derived including reliability function, failure rate, moments and associated measures, quantile function. The model parameters were estimated using the maximum likelihood approach. The performance of the estimation method was assessed via a simulation study. The wind speed datasets were analyzed using new distribution and compare its modeling performance with eleven renowned generalizations of Lindley distributions (Lindley, power Lindley, Marshall–Olkin Lindley, exponentiated Lindley, Pseudo Lindley, Quasi Lindley, Gamma Lindley, generalized inverse Lindley, extended Lindley, exponentiated power Lindley, extended inverse Lindley and extended power Lindley). To good fitting probability distribution function, log-likelihood, root mean square error, coefficient of determination, Akaike Information Criteria for each distribution have been calculated. Additionally, estimated density and cdf curves were fitted over the observed wind speed dataset. Findings showed that the proposed distribution provides the best fitting according to model selection criteria. On the other hand, exponentiated power Lindley and extended power Lindley distribution are the next best distributions for modeling wind speed data for selected stations. Overall, outcomes show the practicality, accuracy, and adequacy of the newly proposed distribution depicting wind energy data.

A new one-parameter model for unit-interval datasets is introduced. The proposed distribution is termed “Unit Xgamma distribution.” Some mathematical properties of the new distribution are derived. We also characterize it using truncated moments and a hazard function. Maximum likelihood, least-squares, weighted least-squares, Anderson- Darling, Cramer-von Mises, and maximum product spacing are among the five estimation methods used to estimate the parameter. A Monte Carlo simulation was used to test the efficacy of these developed estimators. The flexibility of the proposed distribution was assessed using water capacity data. The proposed unit Xgamma distribution can be used for bounded datasets as an alternative to the well-known competitive distributions available in the literature.

In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties including order statistics, hazard rate function, reversed hazard rate function, mode, factorial moments, probability generating function, moment generating function, index of dispersion, Shannon entropy, Mills ratio, mean residual life function, and associated measures are investigated. All these properties can be expressed in explicit forms. It is found that the new probability mass function can be utilized to model positively skewed data with leptokurtic shape. Moreover, the new discrete distribution is considered a proper tool to model equi- and over-dispersed phenomena with increasing hazard rate function. The distribution parameter is estimated by different six estimation approaches, and the behavior of these methods is explored using the Monte Carlo simulation. Finally, two applications to real life are presented herein to illustrate the flexibility of the new model.

In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Andersonӳ-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets ԣoronavirus-flood peaks-forest fire-Leukemia? Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.

In this article, a new two-parameter discrete power-Ailamujia (DsPA) distribution is derived using the survival discretization technique. Some key distributional properties and reliability measures are explored in closed forms, such as probability generating function, first four moments and mean residual life. The DsPA parameters are estimated using the maximum likelihood approach. The performance of this estimation method is assessed via a simulation study. The flexibility of the DsPA distribution is shown using three count datasets. The DsPA distribution provides a better fit than some recent discrete models such as the discrete Burr-Ⅻ, uniform Poisson–Ailamujia, Poisson, discrete-Pareto, discrete-Rayleigh, discrete inverse-Rayleigh, and discrete Burr–Hutke distributions.

The figure shows a schematic of the photocatalytic mechanism of Ba-doped TiO2 QDs.

We propose a new two-parameter discrete model, called discrete Type-II half-logistics exponential (DTIIHLE) distribution using the survival discretization approach. The DTIIHLE distribution can be utilized to model COVID-19 data. The model parameters are estimated using the maximum likelihood method. A simulation study is conducted to evaluate the performance of the maximum likelihood estimators. The usefulness of the proposed distribution is evaluated using two real-life COVID-19 data sets. The DTIIHLE distribution provides a superior fit to COVID-19 data as compared with competitive discrete models including the discrete-Pareto, discrete Burr-XII, discrete log-logistic, discrete-Lindley, discrete-Rayleigh, discrete inverse-Rayleigh, and natural discrete-Lindley.

In this research, a new acceptance sampling plan for a truncated life test is presented, assuming that the quality characteristic follows the power Lomax distribution. The operating characteristic function values are calculated for the proposed sampling plan, jointly with the optimal sample size and the producer’s risk for a selection of distribution parameters. Furthermore, a comparative study with other sampling plans is introduced to demonstrate the advantages of the proposed plan. Finally, a real-life example illustrating the applicability of the proposed sampling plan in a manufacturing company is discussed.

In this study, a discrete inverted Topp-Leone (DITL) distribution is proposed by utilizing the survival discretization approach. The proposed distribution's mathematical features were derived. The maximum likelihood (ML), method of least squares (LS), weighted least squares (WLS), and Cramer Von-Mises (CVM) estimation techniques were used to estimate the parameter. The theoretical results of the ML, LS, WLS, and CVM estimators were demonstrated via a comprehensive simulation study. The proposed DITL distribution has been applied to analyze two count data sets number of deaths due to Covid-19 in Pakistan and India and the findings show the relevance of the proposed distribution.

We study a new continuous distribution called the Marshall-Olkin modified Burr III distribution. The density function of the proposed model can be expressed as a mixture of modified Burr III densities. A comprehensive account of its mathematical properties is derived. The model parameters are estimated by the method of maximum likelihood. The usefulness of the derived model is illustrated over other distributions using a real data set.

Information on wind speed and wind power distribution is significant for a few reasons, for example, surveying wind assets, arranging wind cultivates, and limiting the liabilities for wind power improvement. This study provided an application of a new generalization of two-parameter generalized inverse Lindley distribution using the Marshall–Olkin family for analyzing wind speed and wind power characteristics. Some mathematical properties of the new distribution were studied. We had observed the suitability of new distribution as compared to the other well-known wind speed distributions such as Weibull, inverse exponential, inverted Kumaraswamy, inverse Weibull, inverse Lindley, and generalized inverse Lindley distribution. For this purpose, the time-based wind speed data is taken from the four stations of Pakistan as a case study. We conclude based on certain goodness of fit criteria that the newly developed distribution has a better fit as compared to the other wind speed distributions. Therefore, the new model can be used as an alternative distribution for the assessment of wind speed energy potential.

The most suitable energy source for human use is wind energy which is inexpensive and supports to fulfill the energy demand of the large population. In Pakistan, different wind energy projects are under progress in different potential sites to deal with the energy crises and environmental pollution. Therefore, it is need of the hour to identify all the wind energy potential sites in Pakistan. For that purpose, different wind speed distributions are used. The wind speed distribution is described by the application of probability density functions (pdfs) to evaluate the wind energy potential. The two-parameter Weibull probability density function is used extensively for the applications of wind energy. In this study, we studied the hourly wind speed data for the period of 2017–18 from five different locations in Pakistan is selected for modeling using specific pdfs. The models consist of parametric models that are used for this purpose. The log-likelihood, AIC, BIC, RMSE (root mean square error) and R2 (coefficient of determination) provides the basis for the evaluation of wind speed data with the application of suitable distribution. Results indicate that, Gamma and extreme value distributions provide generally the best fit to the wind speed data for all stations.

We introduced and studied a new three-parameter lifetime distribution based on Marshall–Olkin and inverted Nadarajah–Haghighi distribution. In comparison with some existing lifetime models, the new distribution has very flexible shapes for hazard rate as well as for the probability density function. The related mathematical functions of the new distribution are presented. The maximum likelihood method is considered to obtain the parameter estimates of the MOINH distribution. A simulation study is presented to assess the behavior of the proposed estimator. The potentiality of the distribution is illustrated by fitting two real data sets.

A two-parameter distribution under “Generalized Exponential Uniform Distribution (GEUD)” is proposed in this paper by using the idea of Alzaatreh et al. (2013). We investigate its various properties including its characterization, hazard rate, mean residual life, and Shannon entropy. The constraints on its parameters generate three disjoint subfamilies with regard to their distribution characteristics that exhibit more adaptability when compared with other existing models in the literature for fitting real-life datasets with observations limited in the range (0,1). For the estimation of its parameters, we consider and compare the maximum likelihood, distance minimizing Anderson–Darling, and Cramer–von Mises approaches through simulation studies. To display the importance of this model, we provide its important applications. The GEUD model relative to other models is more suitable in describing certain real datasets.

In this paper, a new three-parameter power inverted Nadarajah–Haghighi distribution is proposed and studied. The new distribution is a generalization of the inverted Nadarajah–Haghighi distribution in which an additional shape parameter is included. Surprisingly, this additional shape parameter dominates the tails’ weights of distribution and also affects skewness and kurtosis. Such heavy-tailed distributions are suitable for fitting actuarial and financial risk real problems. Important mathematical properties of this distribution are obtained. Characterization based on two truncated moments is also derived. The parameters are estimated using the maximum likelihood method. Further, a numerical simulation study is conducted for reinforcement of the results. Finally, the application of the proposed distribution to real-life data sets is presented to prove its applicability.

In this study, a new one-parameter Log-XLindley distribution is proposed to analyze the proportion data. Some of its statistical and reliability properties, including moments with associated measures, hazard rate function, reversed hazard rate, stress strength reliability, and mean residual life function, are investigated in closed forms which help the researchers for modeling data in a small CPU time. It is found that the density function of the introduced distribution can be used as a statistical tool to model asymmetric data. Moreover, the failure rate function can be utilized to model different types of failures, including increasing, bathtub, and J-shaped. The model parameter is estimated using various estimation approaches to get the best estimator to help us in modeling the real data in a good way with high accuracy. A Monte-Carlo simulation study for different sample sizes is performed to assess the performance of the estimations based on some statistical criteria. Finally, two distinctive data sets from SC16 and P3 algorithms, “estimating unit capacity factors,” are analyzed to illustrate the flexibility of the new model.

The Coronavirus Disease (COVID-19) is a respiratory disease that caused a large number of deaths all over the world since its outbreak. The World Health Organization (WHO) has declared the outbreak a global pandemic. The understanding of the random process related to the behavior infection of COVID-19 is an important health and economic problem. In the proposed study, we analyze the frequency of daily confirmed cases of COVID-19 using different two-parameter lifetime probability distributions. We consider the data from the period of March 11, 2020, to July 25, 2020, of Pakistan. We consider nine lifetime probability distributions for the analysis purpose and the selection of best fit was carried out using log-likelihood, AIC, BIC, RMSE, and R2 goodness-of-fit measures. Results indicate that Weibull distribution provides generally the best-fit probability distribution.

A new three-parameter cubic transmuted power distribution is proposed using the cubic rank transformation. The density and hazard functions of the new distribution provide great flexibility. Some mathematical properties of the new model such as quantile function, moments, dispersion index, mean residual life, and order statistics are derived. The model parameters are estimated using five different estimation methods. A comprehensive simulation study is carried out to understand the behavior of derived estimators and choose the best estimation method. The usefulness of the proposed distribution is illustrated using a real dataset. It is concluded that the proposed distribution is better than some well-known existing distributions.

A new class of continuous distributions with two extra shape parameters is introduced named the generalized odd Burr III (GOBIII) family of distributions. The expression of density can be written as a linear combination of exponentiated densities related to baseline model. The basic properties such as ordinary moments, quantile and generating functions, two entropy measures and order statistics are derived. Three special models of proposed family are presented. Characterizations related to truncated moments and hazard function for GOBIII-G distribution are derived. Method of maximum likelihood is used to estimate the model parameters. We study the behaviour of the estimators by means of simulations. The importance of the new family is illustrated using two real data sets. The real data applications suggest that this family can provide better fits than other competitive distributions. The significance of GOBIII-G family lies in its capability to fit symmetric as well as skewed type of data.

This article introduces a new unit distribution namely odd Fréchet power (OFrPF) distribution. Numerous properties of the proposed model including reliability analysis, moments, and Rényi Entropy for the proposed distribution. The parameters of the OFrPF distribution are obtained using different approaches such as maximum likelihood, least squares, weighted least squares, percentile, Cramer-von Mises, Anderson-Darling. Furthermore, a simulation was performed to study the performance of the suggested model. We also perform a simulation study to analyze the performances of estimation methods derived. The applications are used to show the practicality of OFrPF distribution using two real data sets. OFrPF distribution performed better than other competitive models.

The wind energy potential of a specified area can be estimated using wind speed distribution. In this study, the selection of probability density functions is used to model wind speed data recorded at two stations in Pakistan. The suitability of fitted distributions is evaluated using the goodness of fit criterion, power density error, log-likelihood, root mean square error, coefficient of determination, AIC, and BIC. The wind speed data are obtained from two coastal regions of Pakistan at 10m/s average rate for session 2017-2018. Findings indicated that the extended generalized Lindley distribution provide generally the best fit to the wind speed data for both stations. However, it is also observed that power Lindley and extended generalized Lindley distributions have better performance based on power density error criteria in Gwadar and Haripur, respectively.

In this study, a univariate model named as Odd Burr III Weibull distribution is developed. This study explains the behavior of the newly developed model and also presents its failure and survival rate functions. Moreover, some unambiguous expression for ordinary moments, moment generating function, incomplete moments, random number generator, mean deviation, entropies and order statistic are provided in this paper. We also discuss the estimation of parameters by using maximum likelihood estimation method. Finally, two real life applications are also provided to observe the flexibility of observed model as compared to some existing models.