Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data

Inference for the system reliability R is one of the most popular problems in the areas of engineering, statistics, biostatistics and etc. Therefore, there exist considerable numbers of studies concerning this problem. Traditionally, simple random sampling (SRS) is used for estimating the system reliability. However, in recent years, ranked set sampling (RSS), cost effective and efficient alternative of SRS, is used to estimate the system reliability. In this study, we consider the interval estimation of R when both the stress and the strength are independent Weibull random variables based on RSS. We first obtain the asymptotic confidence interval (ACI) of R by using the maximum likelihood (ML) methodology. The bootstrap confidence interval (BCI) of R is also constructed as an alternative to ACI. An extensive Monte-Carlo simulation study is conducted to compare the performances of ACI and BCI of R for different settings. Finally, a real data set is analyzed to demonstrate the implementation of the proposed methods

Kernel-based estimation of P(X >Y) in ranked set sampling

This article is directed at the problem of reliability estimation using ranked set sampling. A nonparametric estimator based on kernel density estimation is developed. The estimator is shown to be superior to its analog in simple random sampling. Monte Carlo simulations are employed to assess performance of the proposed estimator. Two real data sets are analysed for illustration

Estimation of stress-strength reliability for weibull distribution based on type-II right censored ranked set sampling data

In this paper, we consider the estimation of stress-strength reliability R = P (X < Y) under the type-II right censored data when the distributions of both the stress and the strength are Weibull. First, we discuss the estimation of R based on simple random sampling (SRS). Then, we use the effective and the efficient alternative of SRS which is known to be the ranked set sampling (RSS) to estimate R. In the estimation procedure of R, we use two different approaches they are i) maximum likelihood (ML) which requires an iterative method and ii) modified maximum likelihood (MML) which has an explicit form. Monte-Carlo simulation study is performed to identify the efficient sampling method (i.e., SRS or RSS) and the efficient estimation method (i.e., ML or MML). Finally, strength and wind speed data sets are analyzed to illustrate the proposed methods in practice

Spatially Balanced Sampling with Local Ranking

A spatial sampling design determines where sample locations are placed in a study area so that population parameters can be estimated with good precision. Spatially balanced designs draw samples with good spatial spread and provide precise results for commonly used estimators when surveying natural resources. In this article, we propose a new sampling strategy that incorporates ranking information from nearby locations into a spatially balanced sample. If the population exhibits spatial trends, our simple local ranking strategy can improve the precision of commonly used estimators. Numerical results on several test populations with different spatial structures show that local ranking can improve the performance of a spatially balanced design. To show that local ranking is simple and effective in practice, we provide an example application for the health and productivity assessment of a Shiraz vineyard in South Australia. Supplementary materials accompanying this paper appear online

Non-parametric statistical techniques for estimation of regression coefficients and coefficient of variation in corporate finance

Predmet istraživanja disertacije je intervalno ocenjivanje regresionih koeficijenata u prostom linearnom regresionom modelu i kvadratnom regresionom modelu ako slučajna greška nema normalnu raspodelu i intervalno ocenjivanje mera disperzije ako osnovni skup ne sledi normalnu raspodelu. Ako su narušene polazne pretpostavke, proporcija simuliranih intervala za regresione koeficijente i mere disperzije može znatno odstupati od nominalnog nivoa pouzdanosti. U radu su razvijene originalne metode za intervalno ocenjivanje regresionih koeficijenata u prostom linearnom i kvadratnom regresionom modelu zasnovane na Edgeworth-ovom razvoju raspodele t statistika koje se koriste u pomenutim modelima. Dalje, predložene su transformacije metoda koje se koriste za intervalno ocenjivanje koeficijenta varijacije. Reč je o transformaciji zasnovanoj na odsečenoj sredini i bootstrap transformaciji. Validnost predloženih metoda proverena je kroz simulacije koristeći različite raspodele, kao i podatke u oblasti korporativnih finansija. Korporativne finansije obuhvataju praćenje efekata finansiranja kako bi se maksimizirala vrednost kompanije, kao i različite aspekte značajne za rast kompanije. Iz tog razloga, predmet razmatranja prilikom konstrukcije intervalnih ocena bili su podaci o indikatoru verovatnoće bankrotstva, količniku ukupnog duga, meri sistematskog rizika i dividendama. Utvrđeno je da su, u većini razmatranih slučajeva, proporcije simuliranih intervala zasnovanih na predloženim metodama bliže nominalnom nivou pouzdanosti u poređenju sa proporcijama intervala proučavanih u literaturi. Na osnovu rezultata dobijenih u empirijskom delu, date su preporuke za intervalno ocenjivanje koje se mogu koristiti za donošenje pouzdanih zaključaka, pre svega, u oblasti korporativnih finansija. Ključne reči: proporcija simuliranih intervala poverenja, nominalni nivo pouzdanosti, regresioni koeficijent, prost linearni regresioni model, kvadratni regresioni model, koeficijent varijacije, Edgeworth-ov razvoj raspodele t statistike, odsečena sredina, korporativne finansije.The subject of the research of dissertation is the interval estimation of the regression coefficients in the simple linear regression model and quadratic regression model if an error term does not have normal distribution and interval estimation of the measures of dispersion if the population does not follow normal distribution. If the initial assumptions are violated, the proportion of the simulated intervals for the regression coefficients and measures of dispersion can noticeably deviate from the nominal confidence level. The original methods for the interval estimation of the regression coefficients in the simple linear and quadratic regression model, based on the Edgeworth's expansion of the distribution of the t statistics which are used in the mentioned models, were developed. Further, the transformations of the methods used for the interval estimation of the coefficient of variation were proposed. It is about the transformation based on the trimmed mean and the bootstrap transformation. The validation of the proposed methods was checked through simulations using different distributions, as well as the data in the field of corporate finance. Corporate finance includes monitoring the effects of financing in order to maximize a company’s value, as well as various aspects important to the company’s growth. For that reason, the data on the bankruptcy probability indicator, total debt ratio, systematic risk measure and dividends were considered in order to construct the interval estimates. It was found that, in most of the considered cases, the proportions of the simulated intervals based on the proposed methods are closer to the nominal confidence level compared with the proportions of the intervals studied so far in the literature. Based on the results obtained in the empirical part, the recommendations for the interval estimation, which can be used to draw the reliable conclusions, primarily, in the field of corporate finance, were given. Key words: proportion of the simulated confidence intervals, nominal confidence level, regression coefficient, simple linear regression model, quadratic regression model, coefficient of variation, Edgeworth's expansion of the distribution of the t statistic, trimmed mean, corporate finance