Extra Shape Parameter Research Articles

A New Lifetime Distribution and its Application to Cancer Data

Introduction: Recently, researchers have introduced new generated families of univariate lifetime distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution or compounding two distributions to get more flexibility in fitting data in different areas such as medical sciences, environmental sciences, and engineering. The addition of parameter(s) has been proven useful in exploring tail properties and for improving the goodness-of-fit of the family of the proposed distributions. Methods:A new Three-Parameter Weibull-Generalized Gamma distribution which provides more flexibility in modeling lifetime data is developed using a two-component mixture of Weibull distribution (with parameters θ and λ) and Generalised Gamma distribution (with parameters α=4,θ and λ). Some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, moment generating function, Renyi entropy and order statistics are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study is performed to examine the performance of the maximum likelihood estimators of the parameters. Results: Real life applications of the proposed distribution to two cancer datasets are presented and its fit was compared with the fit attained by some existing lifetime distributions to show how the Three-Parameter Weibull-Generalized Gamma distribution works in practice Conclusion: The results suggest that the proposed model performed better than its competitors and it’s a useful alternative to the existing models.

A novel technique for generating families of continuous distributions

In this paper, we present the generalized flexible-G family for creating several continuous distributions. Our new technique features are that it adds only two extra shape parameters to any chosen continuous distribution and is not derived from any parent distribution that currently exists. Several special cases of this family are provided. The generalized flexible-G family offers significant improvements in flexibility, fit, and applicability across a wide range of fields. The family's model parameters are estimated using the maximum likelihood estimation method. A simulation study is conducted to assess the consistency of the maximum likelihood estimates. The generalized flexible log-logistic, a specific case of our novel family, is applied to both patient's analgesia and reliability data in order to illustrate the significance of the family. The generalized flexible log-logistic outperforms several competitive models provided in this paper. Furthermore, the generalized flexible log-logistic performs better than traditional distributions such as the BurrXII, Gumbel, and Weibull models.

New Odd Generalized Exponentiated Exponential-G Family of Distributions

In the last decades, many researchers have developed new methods for generating families of distributions. These generators are obtained by adding one or more extra shape parameter(s) to the baseline distribution to achieve more flexibility for modelling real lifetime data sets. The additional parameter(s) has been proven useful by obtaining tail properties and improving the analysis from the goodness-of-fit for the families of distributions under study. In this paper, we proposed a new family of distributions called the New Odd Generalized Exponentiated Exponential-G Family of Distributions. The statistical properties are derived, and the maximum likelihood estimation technique is described for the proposed new family of distributions. The new models' performance is illustrated by numerical analysis using a real-life dataset, and the dataset shows that the new models offer a better fit compared to other competing models.

Mixture regression modelling based on the shape mixtures of skew Laplace normal distribution

Modelling skewness and heavy-tailedness in heterogeneous data sets is a compelling problem, particularly in regression analysis. The main goal of this study is to propose a mixture regression model based on the shape mixtures of skew Laplace normal (SMSLN) distribution for modelling skewness and heavy-tailedness simultaneously. The SMSLN distribution has been introduced by Doğru and Arslan [Finite mixtures of skew Laplace normal distributions with random skewness. 11th International Statistics Congress (ISC2019); Bodrum/Turkey; Finite mixtures of skew Laplace normal distributions with random skewness. Comput Stat. 2021;36(1):423–447] as a flexible extension of the skew Laplace normal (SLN) distribution and includes an extra shape parameter that controls skewness and kurtosis. The maximum likelihood estimators for the parameters of interest with the help of the expectation-maximization (EM) algorithm are obtained. The performance of the proposed mixture model is demonstrated via a simulation study and a real data example.

Odd Pareto-G Family: Properties, Regression, Simulations and Applications

Several new families have been introduced in the last two decades to extend well-known distributions, and at the same time provide great flexibility for modelling real data. We propose the Odd Pareto-G family with two extra shape parameters, and obtain some of its mathematical properties, which give important information about its structure and may be useful in future research. We construct a new regression model based on a special distribution of the new family. Maximum likelihood estimation and simulations are addressed, and these results show that the estimates are consistent for different percentages of censorship. Four applications to real data show the usefulness of the new models, reveal that they are suitable for the presented data, and can be considered interesting alternatives to model censored and uncensored lifetime data.

Statistical modelling for the Covid-19 mortality rate in the Kingdom of Saudi Arabia

We introduce a new model called the length-biased exponential distribution which become a fascinating new model in a number of research domains in recent years. By adding an extra shape parameter, a new generalised form that is coupled to the length-biased exponential distribution addressed in this work may be constructed, enhancing its utility. The new distribution is known as the new extension length-biased exponential distribution (NELBE). Its density function, as well as its survival and hazard rate curves, are all shown graphically. The study presented the quantile function, linear representations, and some other properties. We displayed and graphed the shapes of the distribution functions. When it came time to calculate the distribution parameters, we employed a total of six distinct estimating strategies. In order to compare and draw conclusions about the performance of the different estimators, a thorough numerical analysis was done. Here, two real data set on COVID-19 mortality rate was examined to show how adaptable and practical the suggested distribution is.

A New Three-Parameter Inverse Weibull Distribution with Medical and燛ngineering Applications

The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility. This addition is beneficial in a variety of fields, including reliability, economics, engineering, biomedical science, biological research, environmental studies, and finance. For modeling real data, several expanded classes of distributions have been established. The modified alpha power transformed approach is used to implement the new model. The data matches the new inverse Weibull distribution better than the inverse Weibull distribution and several other competing models. It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters. Precise expressions for quantiles, moments, incomplete moments, moment generating function, characteristic generating function, and entropy expression are among the determined attributes of the new distribution. The point and interval estimates are studied using the maximum likelihood method. Simulation research is conducted to illustrate the correctness of the theoretical results. Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.

A Modified Power Family of Distributions: Properties, Simulations and Applications

In this paper, we present a new class of distributions called the modified power family by adding an extra shape parameter. Some of its structural properties are derived. Three special cases of the new family are considered and estimated using the method of maximum likelihood. The validity of the method of maximum likelihood is illustrated via Monte Carlo simulations. The importance and flexibility of the new family are empirically illustrated, partly due to efficient modeling of several real data. We compare the proposed family with some distributions and special models generated from other classes using classical statistical measures.

Change point analysis for weighted exponential distribution

The weighted exponential distribution is a distribution that introduce an extra shape parameter to the exponential distribution. It can be used quite effectively to analyze positively skewed data. In this paper, we study a change-point problem of this distribution. The procedures based on Likelihood ratio test, modified information criterion and Schwarz information criterion are studied. Simulations are conducted to indicate the performance of the proposed procedures under different scenarios. Applications on two sets of data are provided to illustrate the detection procedures.

Reliability Analysis of the New Exponential Inverted Topp-Leone Distribution with Applications.

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress–strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.

A new extended log-Weibull regression: Simulations and applications

The induction of one or more parameter(s) in parent distributions opened new doors for flexible modeling in modern distribution theory. Among well-established generalized (G) classes for flexible modeling, the exponentiated-G, Marshall-Olkin-G and odd log-logistic-G families offer induction of one additional parameter while the beta-G and Kumaraswamy-G classes offer two extra shape parameters. The Marshall-Olkin-odd-loglogistic-G (MOOLL-G) family serves as an alternative to the beta-G and Kumaraswamy-G classes. A new motivation for the MOOLL-G family for competing risk scenarios, some useful properties, and parameter estimation are addressed. The new log-MOOLL-Weibull regression is useful for analysis of real life data. The accuracy of the estimates and the residuals is addressed via Monte Carlo simulations. The presented models outperform some other well-known models.

A new generalization of the inverse Lomax distribution with statistical properties and applications

In this paper, we introduce a new generalization of the inverse Lomax distribution with one extra shape parameter, the so-called power inverse Lomax (PIL) distribution, derived by using the power transformation method. We provide a more flexible density function with right-skewed, uni-modal, and reversed J-shapes. The new three-parameter lifetime distribution capable of modeling decreasing, Reversed-J and upside-down hazard rates shapes. Some statistical properties of the PIL distribution are explored, such as quantile measure, moments, moment generating function, incomplete moments, residual life function, and entropy measure. The estimation of the model parameters is discussed using maximum likelihood, least squares, and weighted least squares methods. A simulation study is carried out to compare the efficiencies of different methods of estimation. This study indicated that the maximum likelihood estimates are more efficient than the corresponding least squares and weighted least squares estimates in approximately most of the situations Also, the mean square errors for all estimates are decreasing as the sample size increases. Further, two real data applications are provided in order to examine the flexibility of the PIL model by comparing it with some known distributions. The PIL model offers a more flexible distribution for modeling lifetime data and provides better fits than other models such as inverse Lomax, inverse Weibull, and generalized inverse Weibull.

A generalized transmuted uniform distribution

We introduce a generalized version of the quadratic rank transmuted uniform distribution that generalizes the standard uniform model by incorporating extra shape parameters into its distribution functions. We study the main mathematical and statistical properties of the proposed generalized transmuted uniform model with its estimation and real-life application.

Extended Odd Lomax Family of Distributions: Properties and Applications

The Lomax distribution has a wide range of applications. Due to this, it has had many extensions to render it more flexible and useful to model real world data. In this study, a new family of distributions called the extended odd Lomax family of distributions is introduced by adding two extra shape parameters and one scale parameter. We derived several statistical properties of the new family of distributions. The parameters of the family of distributions are estimated by the use of maximum likelihood method and the consistency of the estimators investigated via Monte Carlo simulations. The usefulness and flexibility of the new family of distributions are illustrated by the use of two real datasets. The results show that the distributions adequately describe the datasets.

The Zeta-G Class: Some Computational and Analytical Aspects

We define a new class of distributions with one extra shapeparameter including some special cases. We provide numerical and computational aspects of the new class. We proposefunctions using the \textsf{R} language to fit any distribution in this family to a data set. In addition, such functions are implemented efficientlyusing the library \textsf{Rcpp} that enables the incorporation of the codes \textsf{C++} in \textsf{R} automatically. Some examples are presentedfor using the implemented routines in practice. We derive some mathematical properties of this class including explicit expressionsfor the moments, generating function and mean deviations. We discuss the estimation of the model parametersby maximum likelihood and provide an application to a real data set.

The Topp Leone Kumaraswamy-G Family of Distributions with Applications to Cancer Disease Data

Background: In the last few years, statisticians have introduced new generated families of univariate distributions. These new generators are obtained by adding one or more extra shape parameters to the underlying distribution to get more flexibility in fitting data in different areas such as medical sciences, economics, finance and environmental sciences. The addition of parameter(s) has been proven useful in exploring tail properties and also for improving the goodness-of-fit of the family of distributions under study. Methods: A new three-parameter family of distributions was introduced by using the idea of T-X methodology. Some statistical properties of the new family were derived and studied. Results: A new Topp Leone Kumaraswamy-G family of distributions was introduced. Two special sub-models, that is, the Topp Leone Kumaraswamy exponential distribution and Topp Leone Kumaraswamy log-logistic distribution were investigated. Two real data sets were used to assess the flexibility of the sub-models. Conclusion: The results suggest that the two sub-models performed better than their competitors.

A Study on A New Type 1 Half-Logistic Family of Distributions and Its Applications

In this paper, we propose a new class of continuous distributions with two extra shape parameters called the a new type I half logistic-G family of distributions. Some of important properties including ordinary moments, quantiles, moment generating function, mean deviation, moment of residual life, moment of reversed residual life, order statistics and extreme value are obtained. To estimate the model parameters, the maximum likelihood method is also applied by means of Monte Carlo simulation study. A new location-scale regression model based on the new type I half logistic-Weibull distribution is then introduced. Applications of the proposed family is demonstrated in many fields such as survival analysis and univariate data fitting. Empirical results show that the proposed models provide better fits than other well-known classes of distributions in many application fields.

Finite mixtures of skew Laplace normal distributions with random skewness

In this paper, the shape mixtures of the skew Laplace normal (SMSLN) distribution is introduced as a flexible extension of the skew Laplace normal distribution which is also a heavy-tailed distribution. The SMSLN distribution includes an extra shape parameter, which controls skewness and kurtosis. Some distributional properties of this distribution are derived. Besides, we propose finite mixtures of SMSLN distributions to model both skewness and heavy-tailedness in heterogeneous data sets. The maximum likelihood estimators for parameters of interests are obtained via the expectation–maximization algorithm. We also give a simulation study and examine a real data example for the numerical illustration of proposed estimators.

A Collocation Method Using Radial Polynomials for Solving Partial Differential Equations

In this article, a collocation method using radial polynomials (RPs) based on the multiquadric (MQ) radial basis function (RBF) for solving partial differential equations (PDEs) is proposed. The new global RPs include only even order radial terms formulated from the binomial series using the Taylor series expansion of the MQ RBF. Similar to the MQ RBF, the RPs is infinitely smooth and differentiable. The proposed RPs may be regarded as the equivalent expression of the MQ RBF in series form in which no any extra shape parameter is required. Accordingly, the challenging task for finding the optimal shape parameter in the Kansa method is avoided. Several numerical implementations, including problems in two and three dimensions, are conducted to demonstrate the accuracy and robustness of the proposed method. The results depict that the method may find solutions with high accuracy, while the radial polynomial terms is greater than 6. Finally, our method may obtain more accurate results than the Kansa method.

The generalized odd Burr III family of distributions: properties, applications and characterizations

ABSTRACTA 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.