Characterization Of Exponential and Power Function Distributions Using Sth Truncated Moments Of Order Statistics (original) (raw)

A Note On Order Statistics from Exponential Power Distribution

International Journal of Algebra and Statistics, 2017

In this paper, we derived probability density function (pdf) for the order statistics from eponential power distribution (EPD). The distribution is flexible at the tail region, because of the presence of shape parameter, which regulates the thickness of the tail. The first moment of the obtained distribution of the order statistics from EPD is presented as well as other measures of central tendencies. This results generalized the results on order statistics from the Laplace distribution and also the results obtained by Arnold, Balakrishnan and Nagaraja on order statistics from normal distribution.

EXPONENTIATED MOMENT EXPONENTIAL DISTRIBUTION AND POWER SERIES DISTRIBUTION WITH APPLICATIONS: A NEW COMPOUND FAMILY

This article introduces a new family of lifetime distributions called the exponentiated moment exponential power series (EMEPS) which generalizes the moment exponential power series (MEPS) proposed by Sadaf (2013). This new family is obtained by compounding the exponentiated moment exponential and truncated power series distributions, where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998). The new family contains some new distributions such as exponentiated moment exponential geometric distribution, exponentiated moment exponential Poisson distribution, exponentiated moment exponential logarithmic distribution and exponentiated moment exponential binomial distribution. Some former works derived by Sadaf 2014 such as moment exponential geometric and moment exponential Poisson distributions are special cases of the new EMEPS family. We obtain several properties of EMEPS family, among them; quantile function, order statistics, moments and entropy. Some special models in the exponentiated moment exponential power series family of distributions are provided. Maximum likelihood (ML) method is applied to obtain parameter estimates of the EMEPS family. A simulation study is carried out to check the consistency of the ML estimators of the parameters. Two real data sets are used to validate the distributions and the results demonstrate that the sub-models from the family can be considered as suitable models under several real situations.

Moments of Power Function Distribution Based on Ordered Random Variables and Characterization

In this paper simple expressions for single and product moments of generalized order statistics from the power function distribution have been obtained. The results for order statistics and records are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional moments of the generalized order statistics is discussed.

A NEW GENERALIZATION OF THE EXPONENTIAL-POISSON DISTRIBUTION USING ORDER STATISTICS

This paperintroduces anew familyof lifetimedistributions, using the ascendant order statistics. The proposed distribution is called the exponential-generalized truncated Poisson (EGTP) distribution. Our approach follows the same procedureasAdamidis and Loukas (1998) and generalizes the exponentialPoisson distribution introduced by Kus (2007). We give general forms of the probability density function (pdf),the cumulative distribution(cdf), the reliabilityand failure ratefunctionsof any order statistics. Theparameters' estimation is attained by the maximum likelihood (ML) and the expectation maximization (EM) algorithms. The appliedstudy is illustrated based onreal datasets.

Characterizations of Continuous Distributions Based on Conditional Expectation of Generalized Order Statistics

Communications in Statistics - Theory and Methods, 2013

Nanda (2010) and Bhattacharjee et al. (2013) characterized a few distributions with help of the failure rate, mean residual, log-odds rate and aging intensity functions. In this paper, we generalize their results and characterize some distributions through functions used by them and Glaser's function. Kundu and Ghosh (2016) obtained similar results using reversed hazard rate, expected inactivity time and reversed aging intensity functions. We also, via w(•)-function defined by Cacoullos and Papathanasiou (1989), characterize exponential and logistic distributions, as well as Type 3 extreme value distribution and obtain bounds for the expected values of selected functions in reliability theory. Moreover, a bound for the varentropy of random variable X is provided.

The Exponentiated Exponential-Geometric Distribution. A distribution with decreasing, increasing and unimodal failure rate

In this paper we proposed a new family of distributions namely Exponentiated Exponential-Geometric (E2G) distribution. The E2G distribution is a straightforwardly generalization of the EG distribution proposed by , which accommodates increasing, decreasing and unimodal hazard functions. It arises on a latent competing risk scenarios, where the lifetime associated with a particular risk is not observable but only the minimum 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, r-th moment of the i-th order statistic, mean residual lifetime and modal value. Maximum likelihood inference is implemented straightforwardly. From a misspecification simulation study performed in order to assess the extent of the misspecification errors when testing the EG distribution against the E2G, and we observed that it is usually possible to discriminate between both distributions even for moderate samples with presence of censoring. The practical importance of the new distribution was demonstrated in three applications where we compare the E2G distribution with several lifetime distributions.

The Generalized Order Statistics from Exponential Distribution

2006

In this paper some distributional properties of the generalized order statistics from two parameter exponential distribution are given. The minimum variance linear unbiased estimators of the parameters and an important characterization of the exponential distribution are presented.

On the Characterizations of Chenrs Two-Parameter Exponential Power Life-Testing Distribution

Journal of Statistical Theory and Applications, 2018

Characterizations of probability distributions play important roles in probability and statistics. Before a particular probability distribution model is applied to fit the real world data, it is essential to confirm whether the given probability distribution satisfies the underlying requirements by its characterization. A probability distribution can be characterized through various methods. In this paper, we provide the characterizations of Chen's two-parameter exponential power life-testing distribution by truncated moment.

Moments of Generalized Order Statistics from Erlang-Truncated Exponential Distribution and its Characterization

In this paper single and product moments of generalized order statistics from Erlang-truncated exponential distribution are studied. Some recurrence relations for both single and product moments of generalized order statistics are also derived. Further the results are deduced for moments of record values and ordinary order statistics and characterization of this distribution through the conditional moment of the generalized order statistics is also presented.

A New Generalized Exponential Distribution: Properties and Applications

International Journal of Analysis and Applications, 2020

The exponential distribution is a popular statistical distribution to study the problems in lifetime and reliability theory. We proposed a new generalized exponential distribution, wherein exponentiated exponential and exponentiated generalized exponential distributions are sub-models of the proposed distribution. We study several important statistical and mathematical properties of the newly developed model and provide the simple expressions for the generating function, moments and mean deviations. Parameters of the proposed distribution are estimated by the technique of maximum likelihood. For two real data sets from the field of biology and engineering, the proposed distribution is compared to some existing distributions. It is found that the proposed model is more suitable and useful to study lifetime data. Thus, it gives us another alternative model for existing models.