On approximation and estimation of distribution function of sum of independent random variables

N. N. Midhu, Isha Dewan, K. K. Sudheesh () and E. P. Sreedevi
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N. N. Midhu: IQVIA
Isha Dewan: Indian Statistical Institute
K. K. Sudheesh: Indian Statistical Institute
E. P. Sreedevi: Maharaja’s College

Statistical Papers, 2024, vol. 65, issue 3, No 11, 1437-1467

Abstract: 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.

Keywords: Convolution; Distribution function; Exact distribution; Non-parametric estimation; Reliability function.; 62E17; 62G05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01413-4

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