In this paper, we discuss a generalization of Balakrishnan skew normal distribution with two parameters that contains the skew-normal, the Balakrishnan skew-normal and the two-parameter generalized skew-normal distributions as special cases. Furthermore, we establish some useful properties and two extensions of this distribution.

In this paper, we discuss a new generalization of univariate skew-Cauchy distribution with two parameters, we denoted this by GSC (l1, l 2), that it has more flexible than the skew-Cauchy distribution (denoted by SC (l)), introduced by Behboodian et al. (2006). Furthermore, we establish some useful properties of this distribution and by two numerical example, show that GSC (l1, l2) can fits the data better than SC (l).

The estimation of unknown parameters of two-parameter Rayleigh distribution based on Type-II progressive censoring with binomial removals is studied. Maximum likelihood estimators of the parameters and their confidence intervals are derived. By applying Markov Chain Monte Carlo techniques, Bayes estimators, and corresponding highest posterior density confidence intervals of parameters are obtained. The expected time required to complete the life test under this censoring scheme is investigated. Monte Carlo simulations are performed to compare the performances of the different methods, and one data set is analyzed for illustrative purposes.

Historically, various methods were suggested for the estimation of Bernoulli and Binomial distributions parameter. One of the suggested methods is the Bayesian method, which is based on employing prior distribution. Their sound selection on parameter space play a crucial role in reducing posterior Bayesian estimator error. At times, large scale of the parametric changes on parameter space brings about an increase in error rate and enlargement of the comparison criteria .therefore, determining appropriate prior distribution on parameter space plays a key part in reducing comparison criteria. Accordingly, in this paper appropriately modified prior distribution was considered for Binomial distribution parameter and then, while extending certain conditions on prior distribution hyper parameters, an effective estimate under the title Expected Bayesian Estimate (AKA E-Bayes) would be proposed. At last, to evaluate the measurement methodologies utilized in this paper, under MSE criteria, extensive simulation studies were conducted, and the results were analyzed and above mentioned methods will be applied in a real example.

Introduction: Lifetime distribution has drawn so much attention in recent research, and this has lead to the development of new lifetime distribution. Addition of parameters to the existing distribution makes the distribution more flexible and reliable and applicable model has become the focus of the recent search. This paper proposed a two-parameter Pranav distribution which has its base from a one-parameter Pranav and Ishita distribution. Methods Two parameter Pranav distribution was proposed. Mathematical and statistical properties of the distribution which includes; moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation, Bonferroni and Lorenz curves were developed. Other lifetime distributions such as Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions were considered in the study. Results: This new distribution was compared with two-parameter Akash, Lindley, one parameter Pranav, Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions to determine the efficiency of the new model. The estimation of parameters has been X-rayed using the method of moments and maximum likelihood. Also, AIC and BIC were used to test for the goodness of fit of the model which was applied to a real-life data of hypertensive patients. The results show that the new two-parameter Pranav distribution has the lowest value of AIC and BIC Conclusion: Based on the AIC and BIC values we can conclude that the two-parameter Pranav is more efficient than the other distribution for modeling survival of hypertensive patients. Hence two-parameter Pranav can be seen as an important distribution in modeling lifetime data.

The standardized precipitation index (SPI) is used vastly for drought monitoring. Among the many of drought indices, the using of SPI for drought events in various time scales is more important. The SPI calculation is based on fitting a probability distribution that describes an observed series of precipitation. There are many models for obtaining probability distribution and parameter estimation, but choosing an appropriate approach is important. This paper employs the four-parameter kappa distribution and techniques of parameters estimation for calculation of SPI. The parameters of kappa distribution are estimated by the genetic algorithm and method of maximum likelihood, and finally the results indicate that the genetic algorithm is more satisfactory for parameters estimation and SPI prediction.