New Family Of Distributions Research Articles

Marshall-Olkin-Odd Power Generalized Weibull-G Family of Distributions with Applications of COVID-19 Data

Attempts have been made to define new families of distributions that provide more flexibility for modeling data that is skewed in nature. In this work, we propose a new family of distributions called Marshall-Olkin-odd power generalized Weibull (MO-OPGW-G) distribution based on the generator pioneered by Marshall and Olkin [20]. This new family of distributions allows for a flexible fit to real data from several fields, such as engineering, hydrology, and survival analysis. The mathematical and statistical properties of these distributions are studied and its model parameters are obtained through the maximum likelihood method. We finally demonstrate the effectiveness of these models via simulation experiments and applications to COVID-19 daily death data sets.

The Gompertz-Topp Leone-G Family of Distributions with Applications

We introduce a new family of distributions, referred to as the Gompertz-Topp-Leone-G (Gom-TL-G) distribution. The new family of distributions can be expressed as an infinite linear combination of the Exp-G distributions. It can handle extremely tailed data and has both monotonic and non-monotonic hazard rate functions. A simulation study is used to assess the estimation method. Some real data examples are analyzed for illustrative purposes.

Marshall-Olkin-Type II-Topp-Leone-G Family of Distributions: Model, Properties and Applications

We develop a new family of distribution called the Marshall-Olkin-Type II-Topp-Leone-G (MO-TII-TL-G) family of distributions, which is a linear combination of the exponential-G family of distributions. The statistical properties of the new distributions are studied and its model parameters are obtainedusing the maximum likelihood method. A simulation study is carried out to determine the performance of the maximum likelihood estimates and lastly real data examples are provided to demonstrate the usefulness of the proposed model in comparison to other models.

Sine-Exponential Distribution: Its Mathematical Properties and Application to Real Dataset

To increase flexibility or to develop covariate models in various ways, new parameters can be added to existing families of distributions or a new family of distributions can be compounded with well-known standard normal distribution. In this paper, a trigonometric-type distribution was developed in order to come up with flexible distribution without adding parameters, considering Exponential distribution as the baseline distribution and Sine-G as the generator. The proposed distribution is referred to as Sine Exponential Distribution. Statistical features, including the moment, moment generating function, entropy, and order statistics were obtained. The proposed distribution's parameters were estimated using the Maximum Likelihood method. Using real datasets, the model's importance was demonstrated. The newly developed model was proven to be better than its competitors.

A More Flexible Asymmetric Exponential Modification of the Laplace Distribution with Applications for Chemical Concentration and Environment Data

In this work, a new family of distributions based on the Laplace distribution is introduced. We define this new family by its stochastic representation as the sum of two independent random variables, one with a Laplace distribution and the other with an exponential distribution. Using a Monte Carlo simulation study, the statistical performance of the estimators obtained by the moments and maximum likelihood methods were empirically evaluated. We studied the coverage probabilities and mean length of the confidence intervals of the corresponding parameters based on the asymptotic normality of these estimators. This simulation study reported a good statistical performance of these estimators. Fits were made to three real data sets with the new distribution, two related to chemical concentrations and one to the environment, comparing it with three similar distributions given in the literature. We have used information criteria for the selection of models. These results showed that the exponentially modified Laplace model can be an alternative distribution to model skewed data with high kurtosis. The new approach is a contribution to the tools of statisticians and various professionals interested in modeling data with high kurtosis.

A new extended distribution: properties, inference and applications in modeling of physical and natural phenomenon

ObjectivesThis paper deals with an extension of the Ishita distribution alongside a new family of distributions based upon the proposed extension. MethodsSome useful properties of the extended Ishita distribution are discussed. Estimation of the parameter has also been done by using different estimation. The extended Ishita distribution has been used to obtain a new family of distributions. Some members of the family have been discussed. Results and conclusionsThe extended Ishita distribution is applied on some real data sets to check the goodness of fit of the distribution. It is found that the proposed distribution is more suitable in modeling the data used as compared with the competing distributions.

The The Gamma Odd Burr X-G Family of Distributions with Applications

A new family of distributions called Gamma Odd Burr X-G (GOBX-G) distribution is introduced in this paper. Its structural properties such as the density expansion, quantile function, moments and generating functions, incomplete moments, probability weighted moments, R´enyi entropy and order statistics were derived. Maximum likelihood technique is used to estimate the parameter of this model and simulation results are provided. The flexibility and applicability of this model is demonstrated using real life datasets.

Combining Two Exponentiated Families to Generate a New Family of Distributions

This article presents a new technique to generate distributions that have the ability to fit any complex data called the exponentiated exponentiated Weibull-X (EEW-X) family, and the exponentiated exponentiated Weibull exponential (EEWE) distribution is presented as a member of this family. The new distribution’s unknown parameters were calculated by applying the maximum likelihood method. Some statistical properties, such as quantile, Rényi entropy, order statistics, and median are obtained for the proposed distribution. A simulation study was performed for different cases to investigate the estimation method’s performance. Three real datasets have been applied in which the new distribution has shown more flexibility compared to some other distributions.

A New Family of Distributions in the Class of the Alpha Power Transformation with Applications to Income

In this paper, a new technique of the alpha-power transformation (APT) is used to propose a new class of probability distribution which is particularly useful for analysis of lifetime data. For the illustrative purposes of the new proposal, a special sub-model of the proposed family is considered in details. Various mathematical properties of the proposed model including quantile function, moments and moment generating function, residual life, mean residual life and order statistics are derived. The maximum likelihood method is used to estimate the unknown parameters. Finally A real data set is analyzed using the new distribution, and a simulation study is carried out to asses the performance of the new family.

A Novel Generalized-M Family: Heavy-Tailed Characteristics with Applications in the Engineering Sector

The Weibull distribution has prominent applications in the engineering sector. However, due to its monotonic behavior of the hazard function, the Weibull model does not provide the best fit for data in many cases. This paper introduces a new family of distributions to obtain new flexible distributions. The proposed family is called a novel generalized- M family. Based on this approach, an updated version of the Weibull distribution is introduced. The updated version of the Weibull distribution is called a novel generalized Weibull distribution. The proposed distribution is able to capture four different patterns of the hazard function. Some mathematical properties of the proposed method are obtained. Furthermore, the maximum likelihood estimators of the proposed family are also obtained. Moreover, a simulation study is conducted for evaluating these estimators. For illustrating the proposed model, two data sets from the engineering sector are analyzed. Based on some well-known analytical measures, it is shown that the novel generalized Weibull distribution is the best competing distribution for analyzing the engineering data sets.

Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data

A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. Several useful statistical properties of the proposed ExpKum-G distribution are derived. Under the classical paradigm, we consider the maximum likelihood estimation under progressive type II censoring to estimate the model parameters. Under the Bayesian paradigm, independent gamma priors are proposed to estimate the model parameters under progressive type II censored samples, assuming several loss functions. A simulation study is carried out to illustrate the efficiency of the proposed estimation strategies under both classical and Bayesian paradigms, based on progressively type II censoring models. For illustrative purposes, a real data set is considered that exhibits that the proposed model in the new class provides a better fit than other types of finite mixtures of exponentiated Kumaraswamy-type models.

The Beta Exponential Power Series Distribution

In this paper, we investigate to propose a new statistical distribution based on power series. We introduce a new family of distributions which are constructed based on a latent complementary risk problem and are obtained by compounding Beta Exponential (BE) and Power Series distributions. The new distribution contains, as special sub-models, several important distributions which are discussed in the literature, such as Beta Exponential Poisson (BEP) distribution, Beta Exponential Geometric (BEG) distribution, Beta Exponential Logarithmic (BEL) distribution, Beta Exponential Binomial (BEB) distribution as special cases. The hazard function of the BEPS distributions can be increasing, decreasing or bathtub shaped among others. The comprehensive mathematical properties of the new distribution is provided such as closed-form expressions for the density, cumulative distribution, survival function, failure rate function, the r-th raw moment, maximum likelihood estimation and also the moments of order statistics. The proposed type of distributions is used to modeling simulated and real datasets.

A More Flexible Reliability Model Based on the Gompertz Function and the Generalized Integro-Exponential Function

This work presents a new distribution that allows modeling data from a random variable with non-negative values. The new family is defined by a stochastic representation of a scaled mixture of a random variable with a Gompertz distribution (G) and a random variable with a uniform distribution on the interval (0,1). The result of this gives rise to a new random variable with a Slash Gompertz (SG) distribution that is more flexible than the Gompertz distribution, that is, it better models atypical data, presenting tails heavier than the Gompertz distribution. The density and some general properties of the resulting family are studied, including its moments and kurtosis coefficient. The inference of the parameters is carried out using the method of moments and maximum likelihood. Finally, illustrations of particular cases of this family are shown, adjusting in this case two sets of real data and estimating the parameters by maximum likelihood, where it is verified that this new family of distributions fits the reliability function better than the distributions of Gompertz (G), Slash Birnbaum Saunders (SBS), Slash Weibull (SW), and Gompertz-Verhults (GV).

A New Useful Exponential Model with Applications to Quality Control and Actuarial Data

The compounding approach is used to introduce a new family of distributions called exponentiated Bell G, analogy to exponentiated G Poisson. Several essential properties of the proposed family are obtained. The special model called exponentiated Bell exponential (EBellE) is presented along with properties. Furthermore, the risk theory related measures including value-at-risk and expected-shortfall are also computed for the special model. Group acceptance sampling plan is designed when a lifetime of a product or item follows an EBellE model taking median as a quality parameter. The parameters of the proposed model are estimated by considering maximum likelihood approach along with simulation analysis. The usefulness of the proposed model is illustrated by practical means which yield better fits as compared to several exponential related extended models.

A Generalized Family of Exponentiated Composite Distributions

In this paper, we propose a new family of distributions, by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new family of distributions, including the moments and the limited moments. Specifically, two special models in this family are discussed. Three real datasets were chosen, to assess the performance of these two special exponentiated-composite models. When fitting to these three datasets, these three special exponentiated-composite distributions demonstrate significantly better performance, compared to the original composite distributions.

The Exponentiated Generalized Alpha Power Family of Distribution: Properties and Applications

In this paper, we introduce the exponentiated generalized alpha power family of distributions to extend the several other distributions. We used the new family to discuss the exponentiated generalized alpha power exponential (EGAPEx) distribution. Some statistical properties of the EGAPEx distribution are obtained. The model parameters are obtained by the maximum likelihood estimation (MLE), maximum product spacing (MPS) and Bayesian estimation methods. A Monte Carlo Simulation is performed to compare between different methods. We illustrate the performance of the proposed new family of distributions by means of two real data sets and the data sets show the new family of distributions is more appropriate as compared to the exponentiated generalized exponential, alpha power generalized exponential, alpha power exponential, generalized exponential and exponential distributions.

Truncated Cauchy Power Weibull-G Class of Distributions: Bayesian and Non-Bayesian Inference Modelling for COVID-19 and Carbon Fiber Data

The Truncated Cauchy Power Weibull-G class is presented as a new family of distributions. Unique models for this family are presented in this paper. The statistical aspects of the family are explored, including the expansion of the density function, moments, incomplete moments (IMOs), residual life and reversed residual life functions, and entropy. The maximum likelihood (ML) and Bayesian estimations are developed based on the Type-II censored sample. The properties of Bayes estimators of the parameters are studied under different loss functions (squared error loss function and LINEX loss function). To create Markov-chain Monte Carlo samples from the posterior density, the Metropolis–Hasting technique was used with posterior density. Using non-informative and informative priors, a full simulation technique was carried out. The maximum likelihood estimator was compared to the Bayesian estimators using Monte Carlo simulation. To compare the performances of the suggested estimators, a simulation study was carried out. Real-world data sets, such as strength measured in GPA for single carbon fibers and impregnated 1000-carbon fiber tows, maximum stress per cycle at 31,000 psi, and COVID-19 data were used to demonstrate the relevance and flexibility of the suggested method. The suggested models are then compared to comparable models such as the Marshall–Olkin alpha power exponential, the extended odd Weibull exponential, the Weibull–Rayleigh, the Weibull–Lomax, and the exponential Lomax distributions.

Properties of a New Generalized Family of Distributions with Application to Relief Times of Patients Data

Statisticians have developed and proposed new families of distributions by extending or generalizing the existing ones. These families of distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime family of distributions called the Extended Topp Leone Generalized Exponentiated-G family of distributions was introduced by using the T-X methodology which has been proposed in the literature. Some mathematical properties of the class of distributions such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions and Renyi entropy were presented. The estimation of the parameters by maximum likelihood method was discussed. Two sub-models such as extended Topp Leone generalized exponentiated exponential and extended Topp Leone generalized exponentiated Weibull distributions were discussed. An application of extended Topp Leone generalized exponentiated exponential distribution to a real life data set representing the relief times (in minutes) of patients receiving an analgesic was used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in this data than the competing models considered.

The Topp-Leone Gompertz-G family of distributions with applications

A new extension of the Topp-Leone distribution is developed to produce a new family of distributions, namely Topp-Leone Gompertz-G distribution. Some of its structural properties including expansion of density, distribution of order statistics, Renyi entropy, moments, quantile, and generating functions are derived. We considered four special cases of the new distribution and we conclude that the distribution can handle heavy tailed data and non-monotonic hazard rate functions. A simulation study was conducted to examine the performance of the special case of the proposed family of distributions. Two lifetime data examples are included in this article to illustrate the applicability of the proposed model in comparison with other competing non-nested models.

The Stacy-G Class: A New Family of Distributions with Regression Modeling and Applications to Survival Real Data

We study the Stacy-G family, which extends the gamma-G class and provides four of the most well-known forms of the hazard rate function: increasing, decreasing, bathtub, and inverted bathtub. We provide some of its structural properties. We estimate the parameters by maximum likelihood, and perform a simulation study to verify the asymptotic properties of the estimators for the Burr-XII baseline. We construct the log-Stacy-Burr XII regression for censored data. The usefulness of the new models is shown through applications to uncensored and censored real data.