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- Title
On approximation and estimation of distribution function of sum of independent random variables.
- Authors
Midhu, N. N.; Dewan, Isha; Sudheesh, K. K.; Sreedevi, E. P.
- Abstract
In this paper, we obtain an approximation for the distribution function of sum of two independent random variables using quantile based representation. The error of approximation is shown to be negligible under some mild conditions. We then use the approximation to obtain a non-parametric estimator for the distribution function of sum of two independent random variables. The exact distribution of the proposed estimator is derived. The estimator is shown to be strongly consistent and asymptotically normally distributed. Extensive Monte Carlo simulation studies are carried out to evaluate the bias and mean squared error of the estimator and also to assess the approximation error. We also compare the performance of the proposed estimator with other estimators available in the literature. Finally, we illustrate the use of the proposed estimator for estimating the reliability function of a standby redundant system.
- Subjects
DISTRIBUTION (Probability theory); RANDOM variables; INDEPENDENT variables; MONTE Carlo method; APPROXIMATION error
- Publication
Statistical Papers, 2024, Vol 65, Issue 3, p1437
- ISSN
0932-5026
- Publication type
Article
- DOI
10.1007/s00362-023-01413-4