Odd Chen Exponential Distribution: Properties and Applications (original) (raw)
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THE ODD MOMENT EXPONENTIAL FAMILY OF DISTRIBUTIONS: ITS PROPERTIES AND APPLICATIONS
International Journal of Applied Mathematics and Statistics, 2018
A new family of continuous distributions called Odd Moment exponential-G family of distributions is proposed. The density and cumulative distribution function are expressed as linear infinite mixtures of exponentiated-G family of the baseline distribution. Some mathematical properties of this new family such as skewness and kurtosis, asymptotes, shapes, moment generating function, distribution of order statistics and power moments are investigated. The model parameter estimation by employing the method of maximum likelihood is discussed. To check the suitability, the proposed model is compared to its submodels and also with useful lifetime models namely the gamma, exponentiated exponential, expo-nentiated moment exponential and beta exponential distributions by conducting three data fitting experiments with real-life data sets.
Odd Generalized Exponential Chen Distributions with Applications
المجلة العلمیة لقطاع کلیات التجارة
The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. The study suggested for the first time, the called Odd generalized-Exponential Chen (OGECD) distribution. The new suggested distribution can have a decreasing and upside-down bathtub failure rate function depending on the value of its parameters; it's including some special sub-model like generalized Pareto distribution and its exponentiated. Some structural properties of the suggested distribution are studied including explicit expressions for the moments. The density function of the order statistics and their moments are obtained. Maximum likelihood is used for estimating the distribution parameters and the observed information matrix is derived. The information matrix is easily numerically determined. Monte Carlo simulations and the application of two real data sets are performed to illustrate the potentiality of this distribution.
ON THE PROPERTIES AND MLEs OF GENERALIZED ODD GENERALIZED EXPONENTIAL- EXPONENTIAL DISTRIBUTION
FUDMA JOURNAL OF SCIENCES, 2021
For proper actualization of the phenomenon contained in some lifetime data sets, a generalization, extension or modification of classical distributions is required. In this paper, we introduce a new generalization of exponential distribution, called the generalized odd generalized exponential-exponential distribution. The proposed distribution can model lifetime data with different failure rates, including the increasing, decreasing, unimodal, bathtub, and decreasing-increasing-decreasing failure rates. Various properties of the model such as quantile function, moment, mean deviations, Renyi entropy, and order statistics. We provide an approximation for the values of the mean, variance, skewness, kurtosis, and mean deviations using Monte Carlo simulation experiments. Estimating of the distribution parameters is performed using the maximum likelihood method, and Monte Carlo simulation experiments is used to assess the estimation method. The method of maximum likelihood is shown to p...
Journal of Data Science
We introduce a new class of distributions called the generalized odd generalized exponential family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Ŕnyi, Shannon and q-entropies, order statistics and probability weighted moments are derived. We also propose bivariate generalizations. We constructed a simple type Copula and introduced a useful stochastic property. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors via a simulation study.
Mathematical and Computational Applications
A new family of continuous distributions called the generalized odd linear exponential family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-F distribution. Important statistical properties such as quantile function, moment generating function, distribution of order statistics, moments, mean deviations, asymptotes and the stress–strength model of the proposed family are investigated. The maximum likelihood estimation of the parameters is presented. Simulation is carried out for two of the mentioned sub-models to check the asymptotic behavior of the maximum likelihood estimates. Two real-life data sets are used to establish the credibility of the proposed model. This is achieved by conducting data fitting of two of its sub-models and then comparing the results with suitable competitive lifetime models to generate conclusive evidence.
Odd Lomax Generalized Exponential Distribution: Application to Engineering and COVID-19 data
Pakistan Journal of Statistics and Operation Research
This paper proposes the 4-parameter odd Lomax generalized exponential distribution for the study of engineering and COVID-19 data. The statistical and mathematical properties of this distribution such as a linear representation of the probability density function, survival function, hazard rate function, moments, quantile function, order statistics, entropy, mean deviation, characteristic function, and average residual life function are established. The estimates of parameters of the proposed distribution are obtained using maximum likelihood estimation (MLE), Maximum product spacings (MPS), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. A Monte-Carlo simulation experiment is carried out to study the MLEs. The applicability of the proposed distribution is evaluated using two real datasets related to engineering and COVID-19. All the computational work was performed in R programming software.
Journal of Statistical Computation and Simulation, 2016
We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.
Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications
Anais da Academia Brasileira de Ciências, 2021
In this paper, a new three-parameter lifetime model called the Topp-Leone odd log-logistic exponential distribution is proposed. Its density function can be expressed as a linear mixture of exponentiated exponential densities and can be reversed-J shaped, skewed to the left and to the right. Further, the hazard rate function of the new model can be monotone, unimodal, constant, J-shaped, constant-increasing-decreasing and decreasing-increasing-decreasing and bathtub-shaped. Our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the proposed model are derived. We briefly describe different estimators namely, the maximum likelihood estimators, ordinary least-squares estimators, weighted least-squares estimators, percentile estimators, maximum product of spacings estimators, Cramér-von-Mises minimum distance estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. Monte Carlo simulations are performed to compare the performance of the proposed methods of estimation for both small and large samples. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to some other well-known distributions.
The odd generalized exponential family of distributions with applications
Journal of Statistical Distributions and Applications, 2015
We propose a new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub. It includes as a special case the widely known exponentiated-Weibull distribution. We present and discuss three special models in the family. Its density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order statistics. For the first time, we obtain the generating function of the Fréchet distribution. Two useful characterizations of the family are also proposed. The parameters of the new family are estimated by the method of maximum likelihood. Its usefulness is illustrated by means of two real lifetime data sets.
A New Modified Generalized Odd Log-Logistic Distribution with Three Parameters
Mathematical theory and modeling, 2018
Statistical distributions are very useful in describing and predicting real-world phenomena. Numerous extended distributions have been extensively used over the last decades for modeling data in many applied sciences such as medicine, engineering and finance. Recent developments focus on defining new families that extend well-known distributions and at the same time provide great flexibility in modeling data in practice. In this paper, we have introduced a new three-parameter exponential distribution called the generalized odd log-logistic-exponential distribution by using the generator defined by Cordeiro et al (2017). This model extends the odd log-logistic-exponential and exponential distributions. Several of its structural properties are discussed in detail. These include shape of the probability density function, hazard rate function, quantile function order statistics, and moments. The method of maximum likelihood is adopted to estimate the model parameters. The applicability ...