Exponential Geometric Distribution Research Articles

Log-Extended Exponential–Geometric Distribution: Moments and Inference Based on Generalized Order Statistics

In this paper, we provide explicit expressions as well as recurrence relations for the single and product moments of generalized order statistics from the log-extended exponential–geometric distribution. These relations are utilized to discuss the special cases of generalized order statistics, and some numerical computations are carried out. Further, we use these results to obtain the best linear unbiased estimators for the location and scale parameters based on progressively Type-II right censored samples. Finally, a real data application is presented.

Dispersion insensitive truncated models for inflated count data with upper bound

Zero-inflated regression models are generally accepted for modeling data with inflated amounts of zeros. The principle used in constructing the distribution for these models has been extended to modeling certain types of data with inflation at the upper bound of the support. An excellent example of this is the zero and κ-inflated truncated Poisson regression model which utilizes the Poisson distribution. However, the equi-dispersion nature of the Poisson distribution makes the model less suitable for data that are under-dispersed and over-dispersed. Models based on exponentiated exponential geometric distribution (EEGD) are presented as alternatives for modeling any count data with an upper bound, irrespective of the nature of dispersion. The models are obtained by truncating the EEGD at the top and inflating at either or both zero and κ. A simulation study is conducted to examine the performances of the models under certain conditions. The result shows that the closer the dispersion parameter c is from the equi-dispersion line, the better the estimates for over-dispersed data, while the farther the dispersion parameter from the equi-dispersed line, the better the estimates for an under-dispersed model. The application of the models is illustrated using data from the Behavioral Risk Factor Surveillance System 2011.

Exponentiated Generalized Exponential Geometric Distribution: Model, Properties and Applications

In this article, a new distribution called Exponentiated Generalized Exponential Geometric Distribution is formulated. We have derived some important mathematical properties like hazard function, probability density function, survival function, quantiles, the measures of skewness based on quartiles and coefficient of kurtosis based on octiles. To estimate the parameters of the new distribution, we have applied the three commonly used estimation methods namely maximum likelihood estimation (MLE), least-square (LSE) method and Cramer-Von-Mises (CVM) method. We have used R programming as well as analytical methods for data analysis. For model validation, we have used different information criteria as Akaike’s information criteria, and Bayesian information criteria (BIC) etc. For the assessment of potentiality of the new distribution, we have considered a real dataset and the goodness-of-fit attained by proposed distribution is compared with some competing distributions. It is found that the proposed model fits the data very well and more flexible as compared to some other models.

Half Cauchy Exponential Geometric Distribution: Model, Properties and Application

In this article, a new distribution called Half Cauchy Exponential Geometric Distribution is introduced. We have derived some important mathematical properties like hazard function, probability density function, survival function, quantiles, the measures of skewness based on quartiles and coefficient of kurtosis based on octiles of the new distribution. To estimate the parameters of the new distribution, we have applied the three commonly used estimation methods namely maximum likelihood estimation (MLE), least-square (LSE) method and Cramer-Von-Mises (CVM) method. We have used R programming as well as analytical methods for data analysis. For the assessment of potentiality of the new distribution, we have considered a real dataset and the goodness-of-fit attained by proposed distribution is compared with some competing distributions.It is found that the proposed model fits the data very well and more flexible as compared to some other models.

The Beta Exponential Power Series Distribution

In this paper, we investigate to propose a new statistical distribution based on power series. We introduce a new family of distributions which are constructed based on a latent complementary risk problem and are obtained by compounding Beta Exponential (BE) and Power Series distributions. The new distribution contains, as special sub-models, several important distributions which are discussed in the literature, such as Beta Exponential Poisson (BEP) distribution, Beta Exponential Geometric (BEG) distribution, Beta Exponential Logarithmic (BEL) distribution, Beta Exponential Binomial (BEB) distribution as special cases. The hazard function of the BEPS distributions can be increasing, decreasing or bathtub shaped among others. The comprehensive mathematical properties of the new distribution is provided such as closed-form expressions for the density, cumulative distribution, survival function, failure rate function, the r-th raw moment, maximum likelihood estimation and also the moments of order statistics. The proposed type of distributions is used to modeling simulated and real datasets.

Moments of progressively type-II censored order statistics from the complementary exponential geometric distribution and associated inference

Moments of progressively type-II censored order statistics from the complementary exponential geometric distribution and associated inference

A new modified exponential-geometric distribution: properties and applications

This paper provides a new three-parameter lifetime distribution with increasing and decreasing hazard function. The various statistical properties of the proposed distribution are also discussed. The maximum likelihood method is used for estimating the unknown parameters, and its performance is assessed using Monte-Carlo simulation. Finally, three real data sets are applied to illustrate the application of the proposed distribution.

A New Long-Term Survival Distribution for Cancer Data

1 1 Universidade Federal de S~ao Carlos and 2 Universidade de S~ao Paulo Abstract: In this paper we propose a new three-parameters lifetime distribu- tion with decreasing hazard function, the long-term exponential geometric distribution. The new distribution arises on latent competing risks scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the minimum lifetime value among all risks, and there is presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its survival and hazard functions, order statistics, Bonferroni function and the Lorenz curve. The parameter estimation is based on the usual maximum likelihood approach. We compare the new distribution with its particular case, the long-term exponential distribution, as well as with the long-term Weibull distribution on two real datasets, observing its poten- tial and competitiveness in comparison with an usual lifetime distribution.

Relations for moments of progressively Type-II censored order statistics from the exponential-geometric distribution and associated inference

In this paper, we derive the recurrence relations for the single and product moments of progressively Type-II right censored order statistics from the exponential-geometric distribution. For a particular case, these results are reduced to the corresponding results for the usual order statistics. Next, we use these moments to obtain the best linear unbiased estimators of the scale and location-scale parameters of the exponential-geometric distribution based on progressively Type-II right censored samples. The best linear unbiased predictors of future failure times are then discussed. Finally, an illustrative example is presented.

Log-extended exponential-geometric parameters estimation using simple random sampling and moving extremes ranked set sampling

In this paper, estimation of parameters α and β for the log-extended exponential-geometric distribution will be respectively considered in cases when β is known and when both are unknown. Simple random sampling (SRS) and moving extremes ranked set sampling (MERSS) will be used, and several traditional estimators will be considered. The estimators using MERSS are compared to the corresponding ones using SRS. The numerical results show that the estimators using MERSS are significantly more efficient than the ones using SRS. A real data set is used for illustration.

A Quantile Regression Model for Bounded Responses Based on the Exponential-Geometric Distribution

A Quantile Regression Model for Bounded Responses Based on the Exponential-Geometric Distribution

The Efficiency of Ranked Set Sampling Design for Parameter Estimation for the Log-Extended Exponential–Geometric Distribution

Cost-effective sampling design is a problem of major concern in some experiments, especially when the measurement of the characteristic of interest is costly or painful or time-consuming. In the current paper, the Fisher information matrix of the log-extended exponential–geometric distribution LEEGD$$(\alpha ,\beta )$$ with parameters $$\alpha $$ and $$\beta $$ based on simple random sample, ranked set sample (RSS), median RSS (MRSS) and extreme RSS is discussed. We obtain the expressions for the Fisher information matrix in each case and use them to perform efficiency comparisons. It is found that MRSS is most efficient when one parameter is inferred at a time (with the other parameter known), while RSS is most efficient when both parameters are inferred simultaneously. A real data set is used for illustration.

Estimation in the Complementary Exponential Geometric Distribution Based on Progressive Type-II Censored Data

Complementary exponential geometric distribution has many applications in survival and reliability analysis. Due to its importance, in this study, we are aiming to estimate the parameters of this model based on progressive type-II censored observations. To do this, we applied the stochastic expectation maximization method and Newton–Raphson techniques for obtaining the maximum likelihood estimates. We also considered the estimation based on Bayesian method using several approximate: MCMC samples, Lindely approximation and Metropolis–Hasting algorithm. In addition, we considered the shrinkage estimators based on Bayesian and maximum likelihood estimators. Then, the HPD intervals for the parameters are constructed based on the posterior samples from the Metropolis–Hasting algorithm. In the sequel, we obtained the performance of different estimators in terms of biases, estimated risks and Pitman closeness via Monte Carlo simulation study. This paper will be ended up with a real data set example for illustration of our purpose.

Two-sided exponential–geometric distribution: inference and volatility modeling

In this paper, two-sided exponential–geometric (TSEG) distribution is proposed and its statistical properties are studied comprehensively. The proposed distribution is applied to the GJR-GARCH model to introduce a new conditional model in forecasting Value-at-Risk (VaR). Nikkei-225 and BIST-100 indexes are analyzed to demonstrate the VaR forecasting performance of GJR-GARCH-TSEG model against the GJR-GARCH models defined under normal, Student-t, skew-T and generalized error innovation distributions. The backtesting methodology is used to evaluate the out-of-sample performance of VaR models. Empirical findings show that GJR-GARCH-TSEG model produces more accurate VaR forecasts than other competitive models.

THE BETA EXPONENTIATED WEIBULL GEOMETRIC DISTRIBUTION: MODELING, STRUCTURAL PROPERTIES, ESTIMATION AND AN APPLICATION TO A CERVICAL INTRAEPITHELIAL NEOPLASIA DATASET

A new distribution, the so called beta exponentiated Weibull geometric (BEWG) distribution is proposed. The new distribution is generated from the logit of a beta random variable and includes the exponentiated Weibull geometric distribution as particular case. 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 model was showed by using a real dataset. In order to validate the results a simulation bootstrap is presented in this paper.

Analysis of a two grade system when Interdecision times have exponential geometric distribution

Consider any single graded marketing organization where depletion of manpower occurssince decisions, exit of personnel etc.. There is an assumption that the depletion due to voluntary exit is correlated. By assuming that the inter-involuntary exit times, inter-breaking decision times forms different modified renewal processes, estimate dmean and estimated variance of time to recruitment are determined. The stochastic model assuming that intercontact times between successive contacts as correlated random variables are proposedShock models with intercontact time have been obtained by assuming the threshold distribution as exponential. In this paper, it is assumed that threshold follows exponentialgeometric distribution.

Generalized linear exponential geometric distributions and its applications

This paper introduces an extension of the generalized linear exponential geometric distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, among others. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution. • A new extended model of GLEG is introduced and studied. • Several reliability and statistical properties are obtained. • The unknown parameters of the new model are estimated. • Some applications in the context of statistics and reliability are provided. • The obtained results are validated using a real data set and it is shown that the new model provides a better fit than some other known distributions.

A New Class of Beta-Complementary Exponential Power Series Distributions

Abstract In this paper, we introduce a new class of beta-complementary exponential power series distributions, which is obtained by replacing the cumulative distribution function of the complementary exponential power series distributions in the logit of a beta random variable. This new class of distributions contains some new submodels, such as beta-complementary exponential geometric, beta-complementary exponential Poisson, beta-complementary exponential binomial, beta-complementary exponential logarithmic, and complementary exponential power series distributions. A general class of distributions is presented and some various properties are obtained in this paper. We characterize the beta-complementary exponential geometric distribution as one of the most applicable distributions in this class. Some mathematical properties of the beta-complementary exponential geometric distribution are reached in terms of the corresponding properties of the complementary exponential geometric and beta exponential distributions. We present expressions for the probability density function, cumulative distribution function, moment generating function, and moments. The estimation of parameters is approached by the maximum likelihood estimation procedure, and the expected information matrix is derived. The flexibility of the distribution is illustrated in application of a real data set.

Moment generating functions of complementary exponential-geometric distribution based on k-th lower record values

Moment generating functions of complementary exponential-geometric distribution based on k-th lower record values

The Kumaraswamy Weibull Geometric Distribution with Applications

‎In this work‎, ‎we study the kumaraswamy weibull geometric ($Kw-WG$) distribution which includes as special cases‎, ‎several models such as the kumaraswamy weibull distribution‎, ‎kumaraswamy exponential distribution‎, ‎weibull geometric distribution‎, ‎exponential geometric distribution‎, ‎to name a few‎. ‎This distribution was monotone and non-monotone hazard rate functions‎, ‎which are useful in lifetime data analysis and reliability‎. ‎We derive some basic properties of the $Kw-WG$ distribution including noncentral $r$th‎-moments, ‎skewness‎, ‎kurtosis‎, ‎generating functions‎, ‎mean deviations‎, ‎mean residual life‎, ‎entropy‎, ‎order statistics and certain characterizations of our distribution‎. ‎The method of maximum likelihood is used for estimating the model parameters and a simulation study to investigate the behavior of this estimation is presented‎. ‎Finally‎, ‎an application of the new distribution and its comparison with recent flexible generalization of weibull distribution is illustrated via two real data sets‎.