The exponentiated generalized inverse Gaussian distribution

Journal of Data Science, 2021

We introduce and study a new four-parameter lifetime model named the exponentiated generalized extended exponential distribution. The proposed model has the advantage of including as special cases the exponential and exponentiated exponential distributions, among others, and its hazard function can take the classic shapes: bathtub, inverted bathtub, increasing, decreasing and constant, among others. We derive some mathematical properties of the new model such as a representation for the density function as a double mixture of Erlang densities, explicit expressions for the quantile function, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R´enyi entropy, density of order statistics and reliability. We use the maximum likelihood method to estimate the model parameters. Two applications to real data illustrate the flexibility of the proposed model.

International Journal of Computational and Theoretical Statistics, 2018

This paper derives a new four-parameter generalized exponential power lifetime probability model for life time data, which generalizes some well-known exponential power lifetime distributions. It is observed that our proposed new distribution bears most of the properties of skewed distributions in reliability and life testing context. It is skewed to the right as well as its failure rate function has the increasing and bathtub shape behaviors. The estimation of the parameters, and simulation and applications of the proposed model have also been discussed.

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.

The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.

Current Trends on Biostatistics & Biometrics , 2019

rest of the article is structured as follows: In section 2, we derive the cumulative distribution function, probability density function, reliability function, odd function, hazard function, reverse hazard function, and cumulative hazard function of the Odd Generalized Exponentiated Inverse Lomax distribution, and present their respective plots for different values of the parameter. In minute details, we establish the structural properties, which include the asymptotic behavior, moments, quantile function, median,

FUPRE Journal of Scientific and Industrial Research (FJSIR), 2019

Lifetime processes has received several attentions recently through modeling the way and manner in which they are distributed. In this article, we propose an extended new generalized exponential distribution for a lifetime processes. The statistical properties of distribution such as kurtosis, survival, hazard, cumulative, odd functions, quantiles, skewness, reversed hazard, and order statistics are derived. The parameters of this class of distribution were also obtained by maximum likelihood method. The behaviour of the model was studied through simulation. Finally, a real life data was used to examine the performance of the propose model. The results show that the model perform favourably well with existing continuous models.

International Journal of Scientific Research in Science, Engineering and Technology, 2020

In the presented work, a continuous distribution consisting of three-parameters is proposed for life-time data called new exponentiated distribution. The discussion of some of the distribution’s statistical as well as mathematical properties, including the Cumulative Distribution Function (CDF), Probability Density function (PDF), quantile function, survival function, hazard rate function, kurtosis measures and skewness, is conducted. The estimation of the presented distribution’s model parameters is performed using the techniques of Cramer-Von-Mises estimation (CVME), least-square estimation (LSE), and maximum likelihood estimation (MLE). The evaluation of the proposed distribution’s goodness of fit is performed through its fitting in comparison with some of the other existing life-time models with the help of a real data set.

Asian Journal of Probability and Statistics, 2018

In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model.

Asian Journal of Probability and Statistics

We propose a new distribution called the extended generalized inverse exponential distribution with four positive parameters, which extends the generalized inverse exponential distribution. We derive some mathematical properties of the proposed model including explicit expressions for the quantile function, moments, generating function, survival, hazard rate, reversed hazard rate and odd functions. The method of maximum likelihood is used to estimate the parameters of the distribution. We illustrate its potentiality with applications to two real data sets which show that the extended generalized inverse exponential model provides a better fit than other models considered.

Journal of Statistical Planning and Inference, 2007

Mudholkar and Srivastava introduced three-parameter exponentiated Weibull distribution. Two-parameter exponentiated exponential or generalized exponential distribution is a particular member of the exponentiated Weibull distribution. Generalized exponential distribution has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions. It is observed that it can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. The genesis of this model, several properties, different estimation procedures and their properties, estimation of the stress-strength parameter, closeness of this distribution to some of the well known distribution functions are discussed in this article.

International Journal of Statistics and Probability

This paper introduces a new generator of probability distribution-the adjusted log-logistic generalized (ALLoG) distribution and a new extension of the standard one parameter exponential distribution called the adjusted log-logistic generalized exponential (ALLoGExp) distribution. The ALLoGExp distribution is a special case of the ALLoG distribution and we have provided some of its statistical and reliability properties. Notably, the failure rate could be monotonically decreasing, increasing or upside-down bathtub shaped depending on the value of the parameters $\delta$ and $\theta$. The method of maximum likelihood estimation was proposed to estimate the model parameters. The importance and flexibility of he ALLoGExp distribution was demonstrated with a real and uncensored lifetime data set and its fit was compared with five other exponential related distributions. The results obtained from the model fittings shows that the ALLoGExp distribution provides a reasonably better fit tha...

Pakistan Journal of Statistics and Operation Research, 2016

The exponentiated gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called the beta exponentiated gamma (BEG) distribution has been introduced. The new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the BEG distribution has been provided. We derived the rth moment and moment generating function for this distribution. Moreover, we discussed the maximum likelihood estimation of this distribution under a simulation study.

2017

This research explored the Exponentiated Generalized Inverse Exponential (EGIE) distribution to include more statistical properties and in particular, applications to real life data as compared with some other generalized models.

Applied Mathematical Modelling, 2013

A new generalization of the linear exponential distribution is recently proposed by Mahmoud and Alam [1], called as the generalized linear exponential distribution. Another generalization of the linear exponential was introduced by Sarhan and Kundu [1,2], named as the generalized linear failure rate distribution. This paper proposes a more generalization of the linear exponential distribution which generalizes the two. We refer to this new generalization as the exponentiated generalized linear exponential distribution. The new distribution is important since it contains as special sub-models some widely well known distributions in addition to the above two models, such as the exponentiated Weibull distribution among many others. It also provides more flexibility to analyze complex real data sets. We study some statistical properties for the new distribution. We discuss maximum likelihood estimation of the distribution parameters. Three real data sets are analyzed using the new distribution, which show that the exponentiated generalized linear exponential distribution can be used quite effectively in analyzing real lifetime data.

In this paper we proposed a new family of lifetime distributions namely complementary exponentiated exponential geometric distribution. This new family arises on a latent competing risk scenario, where the lifetime associated with a particular risk is not observable but only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments, rth moment of the ith order statistic, mean residual lifetime and modal value. Inference is implemented via a straightforwardly maximum likelihood procedure. The practical importance of the new distribution was demonstrated in three applications where our distribution outperforms several former lifetime distributions, such as the exponential, the exponential-geometric, the Weibull, the Modified Weibull and the generalized exponential-Poisson distribution. 1 Several new classes of models have been introduced in recent years grounded in the simple exponential distribution. The main idea is to propose lifetime distributions which can accommodate practical applications where the underlying hazard functions are nonconstant, presenting monotone shapes, since the exponential distribution does not provide a reasonable fit in such situations. For instance, we can cite [3], which proposed a variation of the exponential distribution, the exponential geometric (EG) distribution, with decreasing hazard function, [13], which introduced the exponentiated exponential distribution as a generalization of the usual exponential distribution, which can accommodate data with increasing and decreasing hazard functions, [12], which proposed a generalized exponential distribution, which can accommodate data with increasing and decreasing hazard functions, [21], which proposed the exponentiated type distributions extending the Fréchet, gamma, Gumbel and Weibull distributions, [15], which proposed another modification of the exponential distribution with decreasing hazard function, [5], which generalizes the distribution proposed by [15] by including a power parameter in this distribution, which can accommodate increasing, decreasing and unimodal hazard functions, [19], which proposed the Poisson-exponential distribution, and [17], which proposed the complementary exponential geometric Distribution, which is complementary to the exponential geometric distribution proposed by [3]. The last two proposed distributions accommodate increasing hazard functions. In this paper, following [17], we propose a new distribution family by extending the exponentiated exponential distribution [13] by compounding it with a geometric distribution, hereafter the complementary exponentiated exponential geometric distribution or simplistically the CE2G distribution. The new distribution genesis is stated on a complementary risk problem base [18] in presence of latent risks, in the sense that there is no information about which factor was responsible for the component failure and only the maximum lifetime value among all risks is observed. This family have one shape and two scale parameters accommodating increasing, decreasing and bathtub failure rates.