Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with u
- PDF / 880,780 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 85 Downloads / 181 Views
Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data Cesar Augusto Taconeli1
· Suely Ruiz Giolo1
Received: 7 March 2019 / Accepted: 26 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Ranked set sampling (RSS) has been proved to be a cost-efficient alternative to simple random sampling (SRS). However, there are situations where some measurements are censored, which may not ensure the superiority of RSS over SRS. In this paper, the performance of the maximum likelihood estimators is examined when the data are assumed to follow a Power Lindley or a Weighted Lindley distribution, and are collected according to the original RSS or one of its two variations (the median and extreme RSS). An extensive simulation study, considering uncensored and rightcensored data, and perfect and imperfect ranking, is carried out based on the two mentioned distributions in order to compare the performance of the maximum likelihood estimators from RSS-based designs with the corresponding SRS estimators. Two illustrations are presented based on real data sets. The first involves the lifetimes of aluminum specimens, while the second deals with the amount of spray mixture deposited on the leaves of apple trees. Keywords Monte Carlo simulation · Power Lindley distribution · Weighted Lindley distribution · Extreme ranked set sampling · Median ranked set sampling
1 Introduction Ranked set sampling (RSS), originally proposed by McIntyre (1952), configures an efficient sampling design, relative to the usual simple random sampling (SRS) design, in estimating several population parameters. RSS can be particularly useful when measuring the variable of interest in the sample units is expensive or time consuming,
B
Cesar Augusto Taconeli [email protected] Suely Ruiz Giolo [email protected]
1
Department of Statistics, Federal University of Paraná, Curitiba, Paraná, Brazil
123
C. A. Taconeli, S. R. Giolo
but ranking them according to some cheap and accessible criterion can be done in an efficient way. As an illustration, suppose that we are interested in the lifetime of some type of equipment or system that requires an expensive and/or longstanding destructive test. Moreover, suppose that there is a nondestructive alternative strategy which produces a result strongly correlated with the variable of interest (for example, a similar result obtained through a simulator). Thus, the sample units could be ranked according to their possible lifetimes, but based only on the results which do not involve destruction. Hence, if RSS is used, we can more efficiently choose a set of observations to compose the final sample that will be effectively destructed to evaluate the variable of interest. Several studies have been proved the superiority of RSS and its variations in estimating a great deal of population parameters. For example, Takahasi and Wakimoto (1968), followed by Dell and Clutter (1972), developed the mathematical bas
Data Loading...
