Generalized Mixtures of Exponential Distribution and Associated Inference

A new generalization of the exponential distribution, namely the generalized mixture of exponential distribution, is introduced. Some of its basic properties, such as hazard function, moments, order statistics, mean deviation, measures of uncertainly, and reliability probability, are studied. Three different estimation methods are investigated by the maximum likelihood estimator, least-square estimator, and weighted least-square estimator. The performances of the estimators are assessed by simulation studies. Real-world applications of the proposed distribution are explored, and data fitting results show that the new distribution performs better than its competitors.

Download Full-text

On Erlang-Truncated Exponential Distribution: Theory and Application

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v17i1.2963 ◽

2021 ◽

pp. 155-168

Author(s):

Ibrahim Elbatal ◽

A. Aldukeel

Keyword(s):

Exponential Distribution ◽

Real Data ◽

Moment Generating Function ◽

Likelihood Method ◽

Mean Deviation ◽

Model Parameters ◽

Data Sets ◽

Survival Times ◽

New Distribution ◽

Better Than

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

Download Full-text

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.39 ◽

2020 ◽

pp. 507-522

Author(s):

Parisa Torkaman

Keyword(s):

Least Squares ◽

Exponential Distribution ◽

Mean Squared Error ◽

Weighted Least Squares ◽

Real Data ◽

Minimum Variance ◽

Cumulative Distribution ◽

Estimation Methods ◽

Data Set ◽

Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

Download Full-text

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

Mathematica Slovaca ◽

10.1515/ms-2017-0406 ◽

2020 ◽

Vol 70 (4) ◽

pp. 953-978

Author(s):

Mustafa Ç. Korkmaz ◽

G. G. Hamedani

Keyword(s):

Hazard Function ◽

Mixture Distribution ◽

Real Data ◽

Quantile Function ◽

Estimation Methods ◽

Data Sets ◽

Unknown Parameters ◽

Lorenz Curves ◽

Proposed Model ◽

New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

Download Full-text

HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

EPRA International Journal of Multidisciplinary Research (IJMR) ◽

10.36713/epra3291 ◽

2020 ◽

pp. 276-287

Author(s):

Arun Kumar Chaudhary ◽

Vijay Kumar

Keyword(s):

Exponential Distribution ◽

Likelihood Estimation ◽

Real Data ◽

Least Square ◽

Estimation Methods ◽

Logistic Distribution ◽

Model Parameters ◽

Type I ◽

Data Set ◽

Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

Download Full-text

A New Lifetime Distribution: Properties, Copulas, Applications, and Different Classical Estimation Methods

Complexity ◽

10.1155/2021/6657172 ◽

2021 ◽

Vol 2021 ◽

pp. 1-18

Author(s):

Naif Alotaibi

Keyword(s):

Least Square ◽

Estimation Methods ◽

Mean Deviation ◽

Mean Residual Life ◽

Least Square Estimation ◽

New Model ◽

Inactivity Time ◽

Mean Inactivity Time ◽

The Mean ◽

Anderson Darling

A new continuous version of the inverse flexible Weibull model is proposed and studied. Some of its properties such as quantile function, moments and generating functions, incomplete moments, mean deviation, Lorenz and Bonferroni curves, the mean residual life function, the mean inactivity time, and the strong mean inactivity time are derived. The failure rate of the new model can be “increasing-constant,” “bathtub-constant,” “bathtub,” “constant,” “J-HRF,” “upside down bathtub,” “increasing,” “upside down-increasing-constant,” and “upside down.” Different copulas are used for deriving many bivariate and multivariate type extensions. Different non-Bayesian well-known estimation methods under uncensored scheme are considered and discussed such as the maximum likelihood estimation, Anderson Darling estimation, ordinary least square estimation, Cramér-von-Mises estimation, weighted least square estimation, and right tail Anderson Darling estimation methods. Simulation studies are performed for comparing these estimation methods. Finally, two real datasets are analyzed to illustrate the importance of the new model.

Download Full-text

A New Version of the Exponentiated Exponential Distribution: Copula, Properties and Application to Relief and Survival Times

Statistics Optimization & Information Computing ◽

10.19139/soic-2310-5070-1093 ◽

2021 ◽

Vol 9 (2) ◽

pp. 311-333

Author(s):

Hanaa Elgohari

Keyword(s):

Exponential Distribution ◽

Hazard Function ◽

Real Data ◽

Likelihood Method ◽

Type Model ◽

Data Sets ◽

Survival Times ◽

Mathematical Properties ◽

Mean Variance ◽

New Distribution

In this paper, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index is performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "decreasing", "increasing", "increasing-constant", "upside down-constant", "decreasing nstant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The usefulness and flexibility of the new distribution is illustrated by means of two real data sets.

Download Full-text

The Marshall–Olkin Generalized Inverse Weibull Distribution: Properties and Application

Modern Applied Science ◽

10.5539/mas.v13n2p54 ◽

2019 ◽

Vol 13 (2) ◽

pp. 54

Author(s):

Hamdy M. Salem

Keyword(s):

Weibull Distribution ◽

Hazard Function ◽

Information Matrix ◽

Real Data ◽

Moment Generating Function ◽

Least Square ◽

Superior Performance ◽

Inverse Weibull Distribution ◽

Interval Estimators ◽

New Distribution

In this paper, a new distribution namely, The Marshall–OlkinGeneralized Inverse Weibull Distribution is illustrated and studied. The new distribution is very flexible and contains sub-models such asinverse exponential, inverse Rayleigh, Weibull, inverse Weibull, Marshall–Olkininverse Weibull and Fréchetdistributions. Also, the hazard function of the new distribution can produce variety of forms:an increase, a decrease and an upside-down bathtub. Some properties such as hazard function, quintile function, entropy, moment generating function and order statistics are obtained. Different estimation approaches namely, maximum likelihood estimators, interval estimators, least square estimators, fisher information matrix and asymptotic confidence intervals are described. To illustrate the superior performance of the proposed distribution, a simulation study and a real data analysis are investigated against other models.

Download Full-text

Modeling and estimation on long memory stochastic volatility for index prices of FTSE Bursa Malaysia KLCI

Malaysian Journal of Fundamental and Applied Sciences ◽

10.11113/mjfas.v13n4-1.875 ◽

2017 ◽

Vol 13 (4-1) ◽

pp. 315-324

Author(s):

Kho Chia Chen ◽

Arifah Bahar ◽

Chee-Ming Ting ◽

Haliza Abd Rahman

Keyword(s):

Stochastic Volatility ◽

Long Memory ◽

Financial Time Series ◽

Least Square ◽

Estimation Methods ◽

Fluctuation Analysis ◽

Least Square Estimator ◽

Persistence Properties ◽

Persistence Property ◽

Mean Square Errors

Long memory and volatility have been used to measure risks associated with persistence in financial data sets. However, the persistence in volatility cannot be easily captured because some mathematical models are not able to detect these properties. To overcome this shortfall, this study develops a procedure to construct long-memory stochastic volatility (LMSV) model by using fractional Ornstein-Uhlenbeck (fOU) process in financial time series to evaluate the degree of persistence property of the data. Procedures for constructing the LMSV model and the estimation methods were applied to the real daily index prices of FTSE Bursa Malaysia KLCI over a period of 20 years. The least square estimator (LSE) and quadratic generalised variations (QGV) methods were used to estimate the drift and diffusion coefficient of the volatility process respectively. The long memory parameter was estimated by the detrended fluctuation analysis (DFA) method. The findings show that the volatility of the index prices exhibited a long memory process but the returns of the index prices did not show strong persistence properties. The root mean square errors (RMSE) obtained from various methods indicated that the performances of the model and estimators in describing returns of the index prices were good.

Download Full-text

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

Ibn AL- Haitham Journal For Pure and Applied Science ◽

10.30526/2017.ihsciconf.1815 ◽

2018 ◽

pp. 439

Author(s):

Hazim Mansour Gorgees ◽

Bushra Abdualrasool Ali ◽

Raghad Ibrahim Kathum

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Exponential Distribution ◽

Reliability Function ◽

Bayes Estimator ◽

Likelihood Estimator ◽

Monte Carlo Simulation Technique ◽

Negative Exponential Distribution ◽

Negative Exponential ◽

Better Than

In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

Download Full-text

A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽

10.3390/sym13040679 ◽

2021 ◽

Vol 13 (4) ◽

pp. 679

Author(s):

Jimmy Reyes ◽

Emilio Gómez-Déniz ◽

Héctor W. Gómez ◽

Enrique Calderín-Ojeda

Keyword(s):

Exponential Distribution ◽

Hazard Rate ◽

Rate Function ◽

Estimation Methods ◽

Inverse Gaussian ◽

New Family ◽

Tail Distribution ◽

Zero Values ◽

The Mean ◽

Positive Support

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

Download Full-text