Alpha-Skew-Logistic Distribution

Proyecciones (Antofagasta), 2010

The main object of this paper is to introduce an alternative form of generate asymmetry in the normal distribution that allows to fit unimodal and bimodal data sets. Basic properties of this new distribution, such as stochastic representation, moments, maximum likelihood and the singularity of the Fisher information matrix are studied. The methodology developed is illustrated with a real application.

Journal of science and engineering, 2023

In the domain of the univariate distribution a large number of new distributions were introduced by using different generators. In this paper, a three-parameter distribution called the 'Skew-Lomax' distribution is proposed, which is the special case of the Azzalini distribution to generalize the Lomax distribution. The Lomax distribution is also called Pareto type II distribution, which is a heavy-tailed continuous probability distribution for a non-negative random variable. The statistical properties of the proposed Skew-Lomax distribution, including mean, variance, moments about the origin, cumulative distribution function, hazard rate function, quantile function, and random number generation have been derived. Also, the method of maximum likelihood and the method of moment to estimate the parameters of this distribution have been proposed. Three real data sets have been used to illustrate the usefulness, flexibility, and application of the proposed distribution. The coefficient of determination, chi-square test statistics, and the sum of the square of error depict that the proposed model is more flexible than the Lomax distribution.

International Journal of Pure and Applied Mathematics

The alpha-skew-normal distributions is suggested by D. Elal-Olivero [Proyecciones 29, No. 3, 224–240 (2010; Zbl 1215.62010)]. In this paper, we modify this distribution to a generalized alpha-skew-normal distribution (GASN). Some properties of GASN distributions are investigated.

This paper proposes a new distribution named “The Generalized Alpha Power Exponentiated Inverse Exponential (GAPEIEx for short) distribution” with four parameters, from which one (1) scale and three (3) shape parameters and the statistical properties such as Survival function, Hazard function, Quantile function, r^(th) Moment, Rényi Entropy, and Order Statistics of the new distribution are derived. The method of maximum likelihood estimation (MLE) is used to estimate the parameters of the distribution. The performance of the estimators is assessed through simulation, which shows that the maximum likelihood method works well in estimating the parameters. The GAPEIEx distribution was applied to simulated and real data in order to access the flexibility and adaptability of the distribution, and it happens to perform better than its submodels.

In this paper we discuss different properties of the two generalizations of the logistic distributions, which can be used to model the data exhibiting a unimodal density having some skewness present. The first generalization is carried out using the basic idea of Azzalini [2] and we call it as the skew logistic distribution. It is observed that the density function of the skew logistic distribution is always unimodal and log-concave in nature. But the distribution function, failure rate function and different moments can not be obtained in explicit forms and therefore it becomes quite difficult to use it in practice. The second generalization we propose as a proportional reversed hazard family with the base line distribution as the logistic distribution. It is also known in the literature as the Type-I generalized logistic distribution. The density function of the proportional reversed hazard logistic distribution may be asymmetric but it is always unimodal and log-concave. The distribution function, hazard function are in compact forms and the different moments can be obtained in terms of the ψ function and its derivatives. We have proposed different estimators and performed one data analysis for illustrative purposes.

International Journal of Scientific Research in Science and Technology, 2020

In this article we suggest a new class of skew normal distribution. It will be referred to as Tanh skew-normal distribution, where (Tanh) is a hyperbolic tangent function; a class of skew-normal distribution is proposed by considering a new skew function, It is not a probability distribution function, some properties of this new class distribution have been investigated. Several properties of this distribution have been discussed; parameters estimation using moments, moment generating function, maximum likelihood method, and Fisher information matrix are obtained. A numerical experiment was performed to see the behavior of MLEs. Finally, we apply this model to a real data-set to show that the new class distribution can produce a better fit than other classical Skew normal.

InPrime: Indonesian Journal of Pure and Applied Mathematics

In this paper, a new three-parameter distribution, which is a member of the Alpha Power Transformed Family of distributions, is introduced. The new distribution is a generalization of the logistic model called the alpha power transformed logistic (APTL) distribution. Some mathematical properties of the new distribution like moments, quantile function, median, skewness, kurtosis, Rényi entropy, and order statistics are discussed. The parameters of the distribution are estimated using the maximum likelihood estimation method and a simulation study is performed to investigate the effectiveness of the estimates. The usefulness and flexibility of the APTL distribution in modelling financial data are investigated using two portfolio stock indices, namely the NASDAQ and New York stock indices, both from the United States stock market. Based on the model selection criteria, we are able to establish empirically that the APTL distribution is the best for modelling the two data sets, among the...

2016

A new generalized distribution called gamma Log-logistic Weibull (GLLoGW) distribution is proposed and studied. The GLLoGW distribution include the gamma log-logistic, gamma log-logistic Rayleigh, gamma log logistic exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic as well as other new special cases as sub-models. Some mathematical properties of the new distribution including moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and R\'enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and an application to real data set to illustrates the usefulness of the model is given.

2018

In this study, we propose a new distribution based on the inverted exponential distribution called as “Alpha Power Inverted Exponential” distribution. We provide some of its statistical properties including hazard rate function, quantile function, skewness, kurtosis, and order statistics. The maximum likelihood method is used to estimate the model parameters. We prove empirically the importance and flexibility of the new distribution in modeling with real data applications.

In this paper we discuss six different methods to introduce a shape/skewness parameter in a probability distribution. It should be noted that all these methods may not be new, but we provide new interpretations to them and that might help the partitioner to choose the correct model. It is observed that if we apply any one of these methods to any probability distribution, it may produce an extra shape/skewness parameter to that distribution. Structural properties of these skewed distributions are discussed. For illustrative purposes, we apply these methods when the base distribution is exponential, which resulted in five different generalizations of the exponential distribution. It is also observed that if we combine two or more than two methods successively, then it may produce more than one shape/skewness parameters. Several known distributions can be obtained by these methods and various new distributions with more than one shape parameters may be generated. Some of these new distributions have several interesting properties. and Bever [3], provided a nice interpretations of Azzalini's skew normal distribution as a hidden truncation model. For other univariate and multivariate skewed distributions which have been defined along the same line of Azzalini [1], the readers are referred to Arnold and Bever [4], Gupta and Gupta [9], the recent monograph by Genton [8] and the references cited there.

Statistics, Optimization and Information Computing, 2020

In this paper, a generalized modification of the Kumaraswamy distribution is proposed, and its distributional and characterizing properties are studied. This distribution is closed under scaling and exponentiation, and has some well-known distributions as special cases, such as the generalized uniform, triangular, beta, power function, Minimax, and some other Kumaraswamy related distributions. Moment generating function, Lorenz and Bonferroni curves, with its moments consisting of the mean, variance, moments about the origin, harmonic, incomplete, probability weighted, L, and trimmed L moments, are derived. The maximum likelihood estimation method is used for estimating its parameters and applied to six different simulated data sets of this distribution, in order to check the performance of the estimation method through the estimated parameters mean squares errors computed from the different simulated sample sizes. Finally, four real-life data sets are used to illustrate the usefuln...

Thailand statistician, 2020

This paper proposed a three parameter exponentiated shifted exponential distribution and derived some of its statistical properties including the order statistics and discussed in brief details. Method of maximum likelihood was used to estimate the parameters of the proposed distribution. The proposed distribution was applied on two real life positively skewed data sets with different level of kurtosis and simulation was done. The results obtained indicate that the proposed distribution with unimodal, positively skewed and decreasing shapes property fits better on the data set with higher kurtosis than the data set with lower kurtosis when compared. The simulation results showed that as the sample size increases the biasedness and the mean square error (MSE) of the proposed distribution decreases showing its flexibility property. In both real life applications, the proposed distribution was compared with the three parameter generalized inverted generalized exponential distribution, a three parameter generalized Lindley distribution and the two parameter shifted exponential distribution based on their Alkaike Information Criteria (AIC), Bayesian Information Criteria (BIC), Negative Log-likelihood (NLL) and Hanniquin Information Criteria (HQIC) values and it indicated that the proposed distribution can be used to model real life situations of positively skewed data with high kurtosis. ______________________________

Researchers in the field of statistics have shown a keen interest in developing flexible distributions using generalization or compounding methods. Over the years, many generalized or compounded distributions have been proposed, some of them are: Gompertz Inverse Rayleigh distribution by Halid and Sule (2022) which was developed by extending the inverse Rayleigh distribution using the Gompertz generated family of distribution; Sine BurrXII proposed by Isa et al., (2022) was derived by extending the Burr XII distribution using the Sine G family; Exponentiated Odd Lomax Exponential Distribution by Dhugana and Khumar (2022) which was proposed by compounding an Exponential Odds Function and Lomax Generated family of distributions. Ogunsanya et al., (2021) introduced the Weibull Inverse Rayleigh Distribution by compounding the Inverse Rayleigh Distribution with the Weibull Generated family of distributions. Ahmad et al., (2021) developed the Topp-Leone Power Rayleigh distribution by substituting the Power Rayleigh Distribution into the Topp-Leone family of distribution. Oguntunde et al., (2018) developed the "Gompertz Inverse Exponential Distribution" by compounding the inverse exponential distribution with the Gompertz G family of distribution. Despite the development of these generalized distributions, there are emerging data of interest that exhibit non-normal features like very high skewness and kurtosis. Thus, there is the need to develop more generalized or compound distributions that will have the ability of handling these emerging data of recent times with the stated features. By compounding a well-known standard distribution with a generated family of distribution, the model will be more flexible with high level of skewness and kurtosis to enable the generalized or compounded model have the capability of properly modelling data sets that are heavy tailed or leptokurtic (these are data sets with kurtosis greater than 3). Some of the methods used in developing these flexible models include: Exponentiated family of distribution proposed by Gupta et al. (1998), Beta generated families by Eugene et al.(2002), Transform Transformer (T-X)

Journal of Applied Mathematics, Statistics and Informatics, 2021

In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

International Journal of Statistics and Probability

A new generalized distribution called the {\em log-logistic modified Weibull} (LLoGMW) distribution is presented. This distribution includes many submodels such as the log-logistic modified Rayleigh, log-logistic modified exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh and exponential distributions as special cases. Structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and R\'enyi entropy are derived. Model parameters are estimated based on the method of maximum likelihood. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.