Estimation of P(X ≤ Y ) for discrete distributions with non-identical support

• Autorzy: Mriganka Mouli Choudhury , Rahul Bhattacharya , Sudhansu S. Maiti

Abstrakty

EN

The Uniformly Minimum Variance Unbiased (UMVU) and the Maximum Likelihood (ML) estimations of R = P(X ≤ Y ) and the associated variance are considered for independent discrete random variables X and Y. Assuming a discrete uniform distribution for X and the distribution of Y as a member of the discrete one parameter exponential family of distributions, theoretical expressions of such quantities are derived. Similar expressions are obtained when X and Y interchange their roles and both variables are from the discrete uniform distribution. A simulation study is carried out to compare the estimators numerically. A real application based on demand-supply system data is provided.

Słowa kluczowe

EN

stress-strength model; uniformly minimum variance unbiased; maximum likelihood

• Wydawca: Główny Urząd Statystyczny
• Czasopismo: Statistics in Transition new series
• Rocznik: 2022
• Tom: 23
• Numer: 3
• Strony: 43-64

Daty

wydano

2022

Twórcy

autor

Mriganka Mouli Choudhury

• Visva-Bharati University, Department of Statistics

autor

Rahul Bhattacharya

• University of Calcutta, Department of Statistics

autor

Sudhansu S. Maiti

• Visva-Bharati University, Department of Statistics

Bibliografia

• Ali, M.M, Pal, M, Woo, J, (2005). Inference On P(Y < X ) in Generalized Uniform Distributions. Calcutta Statistical Association Bulletin, 57, pp. 35-48.
• Belyaev, Y, Lumelskii, Y, (1988). Multidimensional Poisson Walks. Journal of Mathematical Sciences, 40, pp. 162-165.
• Barbiero, A, (2013). Inference on Reliability of Stress-Strength Models for Poisson Data. Journal of Quality and Reliability Engineering, 2013, 8 pages.
• Ferguson, S. T, (1967). Mathematical Statistics: A Decision Theoretic Approach. Academic Press.
• Hussain, T, Aslam, M, Ahmad, M, (2016). A Two Parameter Discrete Lindley Distribution. Revista Colombiana de Estadistica, 39(1), pp. 45-61.
• Ivshin, V, V, Lumelskii, Ya, P, (1995). Statistical estimation problems in "Stress-Strength" models.Perm University Press, Perm, Russia.
• Ivshin, V, V, (1996). Unbiased estimation of P(X < Y ) and their variances in the case of Uniform and Two-Parameter Exponential distributions. Journal of Mathematical Sciences, 81, pp. 2790-2793.
• Kotz, S, Lumelskii, Y, Pensky, M, (2003). The stress-strength model and its generalizations. Singapore: World Scientific .
• Lehmann, E. L, Casella, G, (1998). Theory of Point Estimation. New York: Springer.
• Maiti, S.S, (1995). Estimation of P(X ≤ Y ) in geometric case. Journal of Indian Statistical Association, 33, pp. 87-91.
• Obradovic, M, Jovanovic, M, Milosevic, B, Jevremovic, V, (2015). Estimation of P(X ≤ Y ) for Geometric-Poisson model. Hacettepe Journal of Mathematics and Statistics, 44(4), pp. 949-964.
• Rao, C. R, (1973). Linear Statistical Inference and Its Application. John Wiley & Sons, Inc..
• Sathe, Y.S, Dixit, U.J, (2001). Estimation of P(X ≤ Y ) in the negative binomial distribution. Journal of Statistical Planning and Inference, 93, pp. 83-92.

Identyfikatory

DOI

10.2478/stattrans-2022-0029

Biblioteka Nauki

2107147