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Ranked set sampling with unequal set sizes (RSSU) are some of the important variants of ranked set sampling with equal set sizes (RSS). The sets that arise naturally in many applications are typically of different set sizes. One may prefer to use the largest sets available naturally along with the smaller sets rather than an attempt to form artificial equal-sized sets. This article develops maximum likelihood estimators for the location-scale family of distributions based on ranked set sampling with unequal set sizes (RSSU). The closed form expressions for MLE under RSSU do not exist, we have proved the existence of MLE for location and scale parameters for some standard distributions for RSSU data. It is proved that MLE based on MedRSSU are more efficient than their counterparts based on SRS for some standard distributions for location-scale parameters. It is also shown that asymptotic efficiencies of the MLE based on MedRSSU are considerably better than those of the estimators based on RSS with the same number of observations. A simulation study is conducted to compare the performances of the MLE's from RSS and MedRSSU with the corresponding SRS estimators when the underlying distributions are normal and logistic. [ABSTRACT FROM AUTHOR]

In this paper, we present the half logistic inverted Nadarajah–Haghigh (HL-INH) distribution, a novel extension of the inverted Nadarajah–Haghigh (INH) distribution. The probability density function (PDF) for the HL-INH distribution might have a unimodal, right skewness, or heavy-tailed shape for numerous parameter values; however, the shape forms of the hazard rate function (HRF) for the HL-INH distribution may be decreasing. Four specific entropy measurements were investigated. Some useful expansions for the HL-INH distribution were investigated. Several statistical and computational features of the HL-INH distribution were calculated. Using simple (SRS) and ranked set sampling (RSS), the parameters for the HL-INH distribution were estimated using the maximum likelihood (ML) technique. A simulation analysis was executed in order to determine the model parameters of the HL-INH distribution using the SRS and RSS methods, and RSS was shown to be more efficient than SRS. We demonstrate that the HL-INH distribution is more adaptable than the INH distribution and other statistical distributions when utilizing three real-world datasets. [ABSTRACT FROM AUTHOR]

Claims about distributions of time series are often unproven assertions instead of substantiated conclusions for lack of hypotheses testing tools. In this work, Kolmogorov–Smirnov type simultaneous confidence bands (SCBs) are constructed based on simple random samples (SRSs) drawn from realizations of time series, together with smooth SCBs using kernel distribution estimator (KDE) instead of empirical cumulative distribution function of the SRS. All SCBs are shown to enjoy the same limiting distribution as the standard Kolmogorov–Smirnov for i.i.d. sample, which is validated in simulation experiments on various time series. Computing these SCBs for the standardized S&P 500 daily returns data leads to some rather unexpected findings, i.e., student's t-distributions with degrees of freedom no less than 3 and the normal distribution are all acceptable versions of the standardized daily returns series' distribution, with proper rescaling. These findings present challenges to the long held belief that daily financial returns distribution is fat-tailed and leptokurtic. [ABSTRACT FROM AUTHOR]

Background: Population-representative household survey methods require up-to-date sampling frames and sample designs that minimize time and cost of fieldwork especially in low- and middle-income countries. Traditional methods such as multi-stage cluster sampling, random-walk, or spatial sampling can be cumbersome, costly or inaccurate, leading to well-known biases. However, a new tool, Epicentre's Geo-Sampler program, allows simple random sampling of structures, which can eliminate some of these biases. We describe the study design process, experiences and lessons learned using Geo-Sampler for selection of a population representative sample for a kidney disease survey in two sites in Guatemala. Results: We successfully used Epicentre's Geo-sampler tool to sample 650 structures in two semi-urban Guatemalan communities. Overall, 82% of sampled structures were residential and could be approached for recruitment. Sample selection could be conducted by one person after 30 min of training. The process from sample selection to creating field maps took approximately 40 h. Conclusion: In combination with our design protocols, the Epicentre Geo-Sampler tool provided a feasible, rapid and lower-cost alternative to select a representative population sample for a prevalence survey in our semi-urban Guatemalan setting. The tool may work less well in settings with heavy arboreal cover or densely populated urban settings with multiple living units per structure. Similarly, while the method is an efficient step forward for including non-traditional living arrangements (people residing permanently or temporarily in businesses, religious institutions or other structures), it does not account for some of the most marginalized and vulnerable people in a population–the unhoused, street dwellers or people living in vehicles. [ABSTRACT FROM AUTHOR]

Sampling methods in epidemiological studies Sampling allows researchers to obtain information about a population through data obtained from a subset of the population, with a saving in terms of costs and workload compared to a study based on the entire population. Sampling allows the collecting of high quality information, provided that the sample size is large enough to detect a true association between exposure and outcome. There are two types of sampling methods: probability and non-probability sampling. In probability sampling the subset of the population is extracted randomly from all eligible individuals; this method, as all subjects have a chance of being chosen, allows researchers to generalize the findings of their study. In non-probability sampling, some individuals have no chance of being selected, because researchers do not extract the sample from all eligible subjects of a population; the sample is probably non-representative, the effect of sampling error cannot be estimated, so that the study produces non-generalizable results. Examples of probability sampling methods are: simple random sampling, systematic sampling, stratified sampling, and clustered sampling. Examples of non-probability sampling methods are: convenience sampling, judgement sampling. [ABSTRACT FROM AUTHOR]

The mode is a measure of the central tendency as well as the most probable value. Additionally, the mode is not influenced by the tail of the distribution. In the literature the properties and the application of mode estimation is only considered under simple random sampling (SRS). However, ranked set sampling (RSS) is a structural sampling method which improves the efficiency of parameter estimation in many circumstances and typically leads to a reduction in sample size. In this paper we investigate some of the asymptotic properties of kernel density based mode estimation using RSS. We demonstrate that kernel density based mode estimation using RSS is consistent and asymptotically normal with smaller variance than that under SRS. Improved performance of the mode estimation using RSS compared to SRS is supported through a simulation study. An illustration of the computational aspect using a Duchenne muscular dystrophy data set is provided. [ABSTRACT FROM AUTHOR]

In this paper, an estimator of the finite population variance Sy2 is proposed. The proposed estimator is exactly unbiased estimator for Sy2; further, the mean squared error (MSE) of the proposedestimator is derived. Empirical studies from real data sets are usedto compare the proposed estimator and other estimators proposed inthe literature. The proposed estimator is stable among otherfamilies and practically has minimum MSE among other estimators. [ABSTRACT FROM AUTHOR]

Cost-effective and efficient sampling methods are of main concern in many social, biological and environmental studies. In this article, an efficient sampling scheme, named manipulation-based ranked set sampling (MBRSS) scheme is introduced with its properties for estimating population mean and median. The MBRSS is a mixture of simple random sampling (SRS), ranked set sampling (RSS) and median ranked set sampling (MRSS) schemes and is applicable in the situation when ordinary RSS cannot be conducted. It is shown that the proposed scheme provides unbiased mean estimator provided underlying distribution is symmetric. For asymmetric distributions, a weighted mean is proposed, where optimal weights are computed using Shannon's entropy. Monte Carlo simulation is used to ascertain effectiveness of the proposed mean and median estimators in the presence of outliers. We also compared the efficiency of MBRSS and truncation-based ranked set sampling (TBRSS) scheme with respect to SRS under the situation of perfect and imperfect ranking i.e error in rankings with respect to variable of interest. It is observed, on the basis of theoretical and numerical studies that MBRSS is more efficient than SRS. Further, a real data set is used to illustrate the proposed MBRSS scheme. [ABSTRACT FROM AUTHOR]

Kernel density estimation is probably the most widely used non parametric statistical method for estimating probability densities. In this paper, we investigate the performance of kernel density estimator based on stratified simple and ranked set sampling. Some asymptotic properties of kernel estimator are established under both sampling schemes. Simulation studies are designed to examine the performance of the proposed estimators under varying distributional assumptions. These findings are also illustrated with the help of a dataset on bilirubin levels in babies in a neonatal intensive care unit. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a double robust truncation based ranked set sampling (DRTBRSS) for estimating population mean and median. It provides unbiased estimator of population mean under symmetric population and its efficiency dominates the efficiency of conventional estimators based on ranked set sampling (RSS), truncation based rank set sampling (TBRSS) and simple random sampling (SRS). Monte Carlo simulation, based on perfect ranking and ranking based on auxiliary variable, is used under symmetric and asymmetric distributions to evaluate effectiveness of the proposed sampling method. Further, a real data set is used to illustrate the proposed sampling design. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic distribution of the signal-to-noise ratio (SNR) is derived and a new confidence interval for the SNR is introduced. An evaluation of the performance of the new interval compared to Sharma and Krishna (S–K) (1994) confidence interval for the SNR using Monte Carlo simulations is conducted. Data were randomly generated from normal, log-normal, χ2, Gamma, and Weibull distributions. Simulations revealed that the performance of S–K interval is totally dependent on the amount of noise introduced and that it has a constant width for a given sample size. The S–K interval performs poorly in four of the distributions unless the SNR is around one. It is recommended against using the S–K interval for data from log-normal distribution even with SNR = 1. Unlike the S–K interval which does not account for skewness and kurtosis of the distribution, the new confidence interval for the SNR outperforms S–K for all five distributions discussed, especially when SNR ⩾ 2. The proposed ranked set sampling (RSS) instead of simple random sampling (SRS) has improved the performance of both intervals as measured by coverage probability. [ABSTRACT FROM PUBLISHER]

In this paper, an evaluation of the performance of several confidence interval estimators of the population coefficient of variation (τ) using ranked set sampling compared to simple random sampling is performed. Two performance measures are used to assess the confidence intervals for τ, namely: width and coverage probabilities. Simulated data were generated from normal, log-normal, skew normal, Gamma, and Weibull distributions with specified population parameters so that the same values of τ are obtained for each distribution, with sample sizesn=15, 20, 25, 50, 100. A real data example representing birth weight of 189 newborns is used for illustration and performance comparison. [ABSTRACT FROM AUTHOR]

Abstract: The theoretical literature on quantile and distribution function estimation in infinite populations is very rich, and invariance plays an important role in these studies. This is not the case for the commonly occurring problem of estimation of quantiles in finite populations. The latter is more complicated and interesting because an optimal strategy consists not only of an estimator, but also of a sampling design, and the estimator may depend on the design and on the labels of sampled individuals, whereas in iid sampling, design issues and labels do not exist. We study the estimation of finite population quantiles, with emphasis on estimators that are invariant under the group of monotone transformations of the data, and suitable invariant loss functions. Invariance under the finite group of permutation of the sample is also considered. We discuss nonrandomized and randomized estimators, best invariant and minimax estimators, and sampling strategies relative to different classes. Invariant loss functions and estimators in finite population sampling have a nonparametric flavor, and various natural combinatorial questions and tools arise as a result. [Copyright &y& Elsevier]

Ranked set sampling is used to produce a nonparametric kernel estimator of the overlap measure. Some asymptotic properties of the kernel estimator of overlap measure are established. Simulation studies are used to get an insight about the performance of the estimator when the ranked set sampling is used. Illustration using real data is also provided. [ABSTRACT FROM AUTHOR]

Estimation of the parameters of Weibull distribution is considered using different methods of estimation based on different sampling schemes namely, Simple Random Sample (SRS), Ranked Set Sample (RSS), and Modified Ranked Set Sample (MRSS). Methods of estimation used are Maximum Likelihood (ML), Method of moments (Mom), and Bayes. Comparison between estimators is made through simulation via their Biases, Relative Efficiency (RE), and Pitman Nearness Probability (PN). Estimators based on RSS and MRSS have many advantages over those that are based on SRS. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find an optimal alternative bivariate ranked-set sample for one-sample location model bivariate sign test. Our numerical and theoretical results indicated that the optimal designs for the bivariate sign test are the alternative designs with quantifying order statistics with labels {((r+1)/2, (r+1)/2)}, when the set size r is odd and {(r/2+1, r/2), (r/2, r/2+1)} when the set size r is even. The asymptotic distribution and Pitman efficiencies of these designs are derived. A simulation study is conducted to investigate the power of the proposed optimal designs. Illustration using real data with the Bootstrap algorithm for P-value estimation is used. [ABSTRACT FROM AUTHOR]

This article revisits the problem of determining sample size for interval estimation of a binomial proportion. It is motivated by the author's experience as an expert witness in a legal case. The legal case involves a class action suit against a large service provider for alleged over-collection of special service fees. We discuss how: (1) focusing on relative error of the binomial outcome instead of absolute error of the Bernoulli probability p can have a dramatic effect on sample size recommendations, and (2) a year-by-year analysis may differ from a single-year analysis. We also discuss the challenges in presenting such statistical results to nonstatisticians, and propose simplifications to enhance communicability. [ABSTRACT FROM AUTHOR]

Simple random sampling is the foundation for almost every method taught in introductory statistics classes. Many students, however, have difficulty understanding the difference between simple random sampling and cluster sampling and determining whether the assumption of simple random sampling is met, We can find evidence of this difficulty in research articles reporting statistical findings: many analyze the data using simple random sampling assumptions even though a cluster sample was actually taken. We review several statistics texts' treatment of sampling assumptions for confidence intervals and hypothesis tests. We then propose activities that could be used in the classroom to help students gain a better understanding of the concepts of simple random sampling and confidence intervals. [ABSTRACT FROM AUTHOR]

The curve of relationship between fatigue crack growth rate and the stress strength factor amplitude represented an important fatigue property in designing of damage tolerance limits and predicting life of metallic component parts. In order to have a more reasonable use of testing data, samples from population were stratified suggested by the stratified random sample model (SRAM). The data in each stratum corresponded to the same experiment conditions. A suitable weight was assigned to each stratified sample according to the actual working states of the pressure vessel, so that the estimation of fatigue crack growth rate equation was more accurate for practice. An empirical study shows that the SRAM estimation by using fatigue crack growth rate data from different stoves is obviously better than the estimation from simple random sample model. [ABSTRACT FROM AUTHOR]

Four combination methods of independent tests for testing a simple hypothesis versus one-sided alternative are considered viz. Fisher, the logistic, the sum of P-values and the inverse normal method in case of normal distribution. These methods are compared via local power in the presence of nuisance parameters for some values of α using simple random sample. [Copyright &y& Elsevier]

The problem considered is the computation reduction for general delete-d jackknife variance estimators. The delete-d jackknife estimator was proved consistent (Shao and Wu 1986), and in this article its mean squared error is shown to have order o(n[sup -2]), where n is the sample size. These properties are not shared by the traditional delete-1 jackknife in some situations. Use of the delete-d jackknife, however, requires ((Multiple lines cannot be cannot be converted in ASCII text)) recomputations of a point estimate theta, which increases rapidly as n and d increase. Using techniques from survey sampling, a shortcut can be taken with theta evaluated only tn times, m ≪ (Multiple lines cannot be cannot be converted in ASCII text)). The efficiency and consistency of the resulting jackknife-sampling (hybrid) variance estimators (JSVE's) are studied. If m is chosen so that n/m arrow right 0, the increase in mean squared error by using the JSVE is relatively negligible. For the consistency of JSVE, m arrow right Infinity is sufficient. Hence the JSVE with m < n can also be used to alleviate the computational burden for the delete-1 jackknife in the case where n is large and evaluating theta needs large computations. The performance of JSVE is also studied in a simulation study. [ABSTRACT FROM AUTHOR]