Estimation of Jumps, Reliability and Hazard Rate
Murthy, V. K.
Ann. Math. Statist., Tome 36 (1965) no. 6, p. 1032-1040 / Harvested from Project Euclid
Let $F(x)$ be a probability distribution function. Assuming the singular part to be identically zero, it is well known (see e.g. Cramer [1] pp. 52, 53) that $F(x)$ can be decomposed into $F(x) = F_1(x) + F_2(x)$ where $F_1(x)$ is an everywhere continuous function and $F_2(x)$ is a pure step function with steps of magnitude, say, $S_\nu$ at the points $x = x_\nu, \nu = 1, 2, \cdots, \infty$ and that finally both $F_1(x)$ and $F_2(x)$ are non-decreasing and are uniquely determined. In this paper the problem of estimating the jump $S_i$ corresponding to the saltus $x = x_i$ is considered. Also considered are the problems of estimation of reliability and hazard rate. Based on a random sample $X_1, X_2, \cdots X_n$ of size $n$ from the distribution $F(x)$, consistent and asymptotically normal classes of estimators are obtained for estimating the jump $S_i$ corresponding to the saltus $x = x_i$. Based on the earlier work of the author [2] on estimation of probability density, consistent and asymptotically normal estimates are obtained for the reliability and hazard rate.
Publié le : 1965-06-14
Classification: 
@article{1177700075,
     author = {Murthy, V. K.},
     title = {Estimation of Jumps, Reliability and Hazard Rate},
     journal = {Ann. Math. Statist.},
     volume = {36},
     number = {6},
     year = {1965},
     pages = { 1032-1040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177700075}
}
Murthy, V. K. Estimation of Jumps, Reliability and Hazard Rate. Ann. Math. Statist., Tome 36 (1965) no. 6, pp.  1032-1040. http://gdmltest.u-ga.fr/item/1177700075/