‎Censored samples are discussed in experiments of life-testing; i.e‎. ‎whenever the experimenter does not observe the failure times of all units placed on a life test‎. ‎In recent years‎, ‎inference based on censored sampling is considered‎, ‎so that about the parameters of various distributions such as ‎normal‎, ‎exponential‎, ‎gamma‎, ‎Rayleigh‎, ‎Weibull‎, ‎log normal‎, ‎inverse Gaussian‎, ‎logistic‎, ‎Laplace‎, ‎and Pareto‎, ‎has been inferred based on censored sampling‎.

‎In this paper‎, ‎a procedure for exact hypothesis testing and obtaining confidence interval for mean of the exponential distribution under Type-I progressive hybrid censoring is proposed‎. ‎Then‎, ‎performance of the proposed confidence interval is evaluated using simulation‎. ‎Finally‎, ‎the proposed procedures are performed on a data set‎.

 ‎A Poisson distribution is well used as a standard model for analyzing count data‎. ‎So the Poisson distribution parameter estimation is widely applied in practice‎. ‎Providing accurate confidence intervals for the discrete distribution parameters is very difficult‎. ‎So far‎, ‎many asymptotic confidence intervals for the mean of Poisson distribution is provided‎. ‎It is known that the coverage probability of the confidence interval (L(X),U(X)) is a function of distribution parameter‎. ‎Since Poisson distribution is discrete‎, ‎coverage probability of confidence intervals for Poisson mean has no closed form and the exact calculation of confidence coefficient‎, ‎average coverage probability and maximum coverage probabilities for this intervals‎, ‎is very difficult‎. ‎Methodologies for computing the exact average coverage probabilities as well as the exact confidence coefficients of confidence intervals for one-parameter discrete distributions with increasing bounds are proposed by Wang (2009)‎. ‎In this paper‎, ‎we consider a situation that the both lower and upper bounds of the confidence interval is increasing‎. ‎In such situations‎, ‎we explore the problem of finding an exact maximum coverage probabilities for confidence intervals of Poisson mean‎. ‎Decision about confidence intervals optimality‎, ‎based on simultaneous evaluation of confidence coefficient‎, ‎average coverage probability and maximum coverage probabilities‎, ‎will be more reliable‎.