We introduce a new wrapped EXPONENTIAL DISTRIBUTION named transmuted wrapped EXPONENTIAL (TWE) DISTRIBUTION, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped DISTRIBUTION with this study. The introduced DISTRIBUTION is more flexible than traditional wrapped EXPONENTIAL DISTRIBUTION. The paper provides the explicit form of important DISTRIBUTIONal properties of the introduced DISTRIBUTION such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Ré nyi and Shannon entropies are also obtained. The statistical inference problem for the TWE DISTRIBUTION is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis.

In this article, a new censoring scheme is considered, namely, a middle part of a random sample is censored. A treatment for reconstructing the missing order statistics is investigated. The proposed procedure is studied in detail under EXPONENTIAL DISTRIBUTION which is widely used as a constant failure model in reliability.Different approaches are used to obtain point and interval reconstructors and then they are compared. A numerical example is presented for illustrating all the proposed inferential procedures. Eventually, we present some remarks including how the results of the paper can be used when the parameters of the EXPONENTIAL DISTRIBUTION are unknown.

A new generalized version of the mixed Poisson DISTRIBUTION, called the Poisson-beta EXPONENTIAL (PBE) DISTRIBUTION, is obtained by mixing the Poisson and the beta EXPONENTIAL (BE) DISTRIBUTIONs. Estimation of the parameters, using the method of moments and maximum likelihood estimators, is discussed. We show the consistency of the new model parameters using simulation study. Examples are given for fitting the PBE DISTRIBUTION to data, and the fit model is compared with that obtained using other DISTRIBUTIONs.

The EXPONENTIAL DISTRIBUTION is a popular model in applications to real data. We propose a new extension of this DISTRIBUTION, called the Lomax-EXPONENTIAL DISTRIBUTION, which presents greater flexibility to the model. Also there is a simple relation between the Lomax-EXPONENTIAL DISTRIBUTION and the Lomax DISTRIBUTION. Results for moment, limit behavior, hazard function, Shannon entropy and order statistic are provided. To estimate the model parameters, the method of maximum likelihood and Bayse estimations are proposed. Two data sets are used to illustrate the applicability of the Lomax-EXPONENTIAL DISTRIBUTION.

The problem of distinguishing between DISTRIBUTIONs is always important. It becomes more complicated when data is contaminated by outliers. Here, we use two well-known Lindley and EXPONENTIAL DISTRIBUTIONs infected by outliers. The closeness of the Lindley DISTRIBUTION in comparison with the EXPONENTIAL DISTRIBUTION with outliers is discussed in this research. Three ways such as likelihood ratio, asymptotic likelihood ratio tests and minimum Kolmogorov distance are used to select the proper fitted model for a real data set. We perform Monte Carlo simulation to obtain the probability of correct selection for various values of sample sizes and parameters based on the best criteria in the DISTRIBUTIONs. In general, it has been seen that the Lindley DISTRIBUTION is closer to EXPONENTIAL DISTRIBUTION contaminated by outliers based on the likelihood ratio and Kolmogorov criteria. An actual example of real data is used to see the behaviour of the DISTRIBUTIONs.

We propose a novel parametric DISTRIBUTION, termed the Beta Modified EXPONENTIAL Power Series (BMEPS) DISTRIBUTION, capable of modeling increasing, decreasing, bathtub-shaped, and unimodal failure rates. Constructed from addressing a latent complementary risk problem, this DISTRIBUTION arises from a combination of the Beta Modified EXPONENTIAL (BME) and power series DISTRIBUTIONs. Within this new DISTRIBUTION, several important DISTRIBUTIONs discussed in the literature, such as the Beta Modified EXPONENTIAL Poisson (BMEP), Beta Modified EXPONENTIAL Geometric (BMEG), and Beta Modified EXPONENTIAL Logarithmic (BMEL) DISTRIBUTIONs, exist as special submodels. This work provides a comprehensive mathematical treatment of the new DISTRIBUTION, offering closed-form expressions for its density, cumulative DISTRIBUTION, survival function, failure rate function, the r-th raw moment, and moments of order statistics. Furthermore, we delve into maximum likelihood estimation and present formulas for the elements comprising the Fisher information matrix. Finally, to showcase the flexibility and potential applicability of the new DISTRIBUTION, we apply it to a real dataset.