Estimation of P{X ≤ Y } for Geometric-Poisson Model
نویسندگان
چکیده
In this paper we estimate R = P{X ≤ Y } when X and Y are independent random variables from geometric and Poisson distribution respectively. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. A procedure for deriving bootstrap confidence intervals is presented. UMVUE of R and UMVUE of its variance are derived and also the Bayes estimator of R for conjugate prior distributions is obtained. Finally, we perform a simulation study in order to compare these estimators. keywords: stress-strength, geometric distribution, Poisson distribution, maximum likelihood estimator, Bayes estimator, UMVUE, bootstrap confidence intervals. MSC(2010): 62F10, 62F12, 62F15, 62F25, 62F40.
منابع مشابه
Reliability Estimates of Generalized Poisson Distribution and Generalized Geometric Series Distribution
Discrete distributions have played an important role in the reliability theory. In order to obtain Bayes estimators, researchers have adopted various conventional techniques. Generalizing the results of Maiti (1995), Chaturvadi and Tomer (2002) dealt with the problem of estimating P{X1, X2, …, Xk ≤ Y}, where random variables X and Y were assumed to follow a negative binomial distribution. Agit ...
متن کاملExact maximum coverage probabilities of confidence intervals with increasing bounds for Poisson distribution mean
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 coverag...
متن کاملSome weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
متن کاملInteger Valued AR(1) with Geometric Innovations
The classical integer valued first-order autoregressive (INA- R(1)) model has been defined on the basis of Poisson innovations. This model has Poisson marginal distribution and is suitable for modeling equidispersed count data. In this paper, we introduce an modification of the INAR(1) model with geometric innovations (INARG(1)) for model- ing overdispersed count data. We discuss some structu...
متن کاملBayesian change point estimation in Poisson-based control charts
Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step < /div> change, a linear trend and a known multip...
متن کامل