Product Moments Of Order Statistics Research Articles

A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling

In survival and stochastic lifespan modeling, numerous families of distributions are sometimes considered unnatural, unjustifiable theoretically, and occasionally superfluous. Here, a novel parsimonious survival model is developed using the Bilal distribution (BD) and the Kavya-Manoharan (KM) parsimonious transformation family. In addition to other analytical properties, the forms of probability density function (PDF) and behavior of the distributions' hazard rates are analyzed. The insights are theoretical as well as practical. Theoretically, we offer explicit equations for the single and product moments of order statistics from Kavya-Manoharan Bilal Distribution. Practically, maximum likelihood (ML) technique, which is based on simple random sampling (SRS) and ranked set sampling (RSS) sample schemes, is employed to estimate the parameters. Numerical simulations are used as the primary methodology to compare the various sampling techniques.

On the Generalized Bilal Distribution: Some Properties and Estimation under Ranked Set Sampling

The generalized Bilal (GB) distribution can be defined as the distribution of the median of three independent random variables drawn from the Weibull distribution. Its failure rate function can be monotonic (decreasing or increasing) or upside-down bathtub-shaped. In this study, we aim to reveal some important properties of the GB distribution that have not been considered before. The findings are both theoretical and practical. From the theoretical viewpoint, we present explicit expressions for both single and product moments of order statistics from the GB distribution. The L-moments are derived as well. From the practical viewpoint, the parameter estimations are accomplished using the maximum likelihood (ML) method, which is based on two different sampling schemes: simple random sampling (SRS) and ranked set sampling (RSS) schemes. Furthermore, the asymptotic confidence intervals for the SRS and RSS estimators are discussed. For the sake of comparison and illustration, a simulation study and a real data example are presented. Concluding remarks are given at the end.

On the order statistics of exponentiated moment exponential distribution and associated inference

Explicit algebraic expressions for both single and product moments of order statistics from the exponentiated moment exponential (EME) distribution are derived. By using these expressions, we have computed the means, variances and covariances of order statistics for and for arbitrarily chosen parameter values. Further, these moments are used to determine the best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) of the location and scale parameters based on complete as well as Type-II right censored samples. Prediction of unobserved order statistics in Type-II right censored samples is also discussed. A simulation study and a real data example are presented for the sake of comparison and illustration. The concluding remarks are given at the end.

Order Statistics from the Ishita distribution and Associated Inference

Ishita distribution proposed by Shankar and Shukla (2017) is useful in modelling data from biomedical science and engineering and it is also useful for the analysis of Stress-strength reliability of a component. It gives the best fit than most of the distributions such as Lindley, exponential and Akash distributions. In this paper, we have derived the recurrence relations and exact expressions for single and product moments of order statistics from Ishita distribution. By using exact expressions, we have tabulated the means, variances and covariance’s of order statistics from Ishita distribution. Further, using these moments, we have obtained the best linear unbiased estimators (BLUEs) for the location and scale parameters of the Ishita distribution based on the type-II censored samples.

Moments of order statistics and k-record values arising from the complementary beta distribution with application

The order statistics (OSs) arise in both practical and theoretical aspects including goodness-of-fit tests, characterizations of probability distributions and some estimation approaches such as the L-moments method. Most of these instances are connected with moments of OSs. The records and k-record statistics, also called kth record values in the literature, are other important topics related to the OSs. This kind of data appears in some practical circumstances, e.g. shock models, industrial stress testing and meteorological data analysis. This paper deals with deriving recurrence relations for the single and the product moments of OSs as well as k-record values from the complementary beta (CB) distribution defined by Jones (2002). The CB model, as a distribution on the unit interval, is more flexible than the well-known beta distribution in problems involving moments of OSs. This fact suggests that the former distribution can be employed rather than the latter when OSs are of the main interest. The results obtained are applied on four real data sets for the issues of parameter estimation as well as providing a visual inspection for goodness-of-fit of the CB model.

Inferences for the Type-II Exponentiated Log-Logistic Distribution Based on Order Statistics with Application

In this paper, we first derive the exact explicit expressions for the single and product moments of order statistics from the type-II exponentiated log-logistic distribution, and then use these results to compute the means, variances, skewness and kurtosis of rth order statistics. Besides, best linear unbiased estimators (BLUEs) for the location and scale parameters for the type-II exponentiated log-logistic distribution with known shape parameters are studied. Finally, the results are illustrated with a real data set.

Recurrence relations for moments of order statistics from half logistic-geometric distribution and their applications

The half logistic-geometric (HLG) distribution derived here is a simple distribution with interesting properties and is therefore a useful distribution for analyzing lifetime data. Algorithm is derived for the computation of single and product moments of order statistics from this distribution. These recurrence relations enable the computation of means, variances and covariances of all order statistics for all sample size in a simple and efficient way. The results are of great importance in determining the best linear unbiased estimator of the scale parameter of a scaled-HLG distribution, and those of parameters of the more general location-scale HLG distribution based on complete and Type-II censored samples. Finally, an example is presented to illustrate the developed results.

A Note on Exact Moments of Order Statistics from Exponentiated Burr XII Distribution

In this paper, we establish the explicit expressions and some recurrence relations for single and product moments of order statistics from exponentiated Burr XII distribution. By using, these results we can calculate the mean and variances based on order statistics for the given distribution.

Inference for generalized inverse Lindley distribution based on generalized order statistics

This article addresses the problem of deriving the explicit expressions for single and product moments of order statistics, generalized order statistics and dual generalized order statistics from the generalized Lindley distribution. The means and variances of order statistics, lower record values and progressively type-II censored order statistics for various values of the parameters are tabulated. Furthermore, the maximum likelihood estimators for the parameters of the model using generalized order statistics are obtained. The Bayes estimators under squared error and LINEX (Linear exponential) loss functions using Markov Chain Monte Carlo (MCMC) technique are obtained. Finally, three real data examples to lower record values, type-II censored and progressively type-II censored order statistics have been analyzed for illustrative purposes.

Moments of Order Statistics from Length-Biased Exponential Distribution and Associated Inference

Dara and Ahmad (Recent advances in moment distribution and their hazard rates, Academic Publishing GmbH KG, Lap Lambert, 2012) proposed the length-biased exponential (LBE) distribution and proved that the LBE distribution is more flexible than the exponential distribution. In this paper, we have obtained new explicit algebraic expressions and some recurrence relations for both single and product moments of order statistics from LBE distribution. Further, these expressions are used to compute the means, variances and covariances of order statistics for different sample of sizes and for arbitrarily chosen parameter values. Next, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on complete as well as Type-II right censored samples. Finally, we carried out a simulation study to show the application of our results.

On Moments of Lindley Distribution Based on Generalized Order Statistics

In this paper, we have deduced the exact and explicit expressions for single and product moments of Lindley distribution based on generalized order statistics in terms of Gauss hypergeometric function and Kampé de Fériet series. These results include the exact expression for the single and product moments of order statistics, progressive Type II censoring, record values Pfeifer’s record value and sequential order statistics from Lindley distribution. Further, means and variances of Lindley distribution based on order statistics, progressive type II censored order statistics and for generalized order statistics have been computed. We have also calculated the best linear unbiased estimators for location and scale parameters of Lindley distribution utilizing these results. Finally, a real data application is given.

Accurate computation of single and product moments of order statistics under progressive censoring

ABSTRACTAn accurate procedure is proposed to calculate approximate moments of progressive order statistics in the context of statistical inference for lifetime models. The study analyses the performance of power series expansion to approximate the moments for location and scale distributions with high precision and smaller deviations with respect to the exact values. A comparative analysis between exact and approximate methods is shown using some tables and figures. The different approximations are applied in two situations. First, we consider the problem of computing the large sample variance–covariance matrix of maximum likelihood estimators. We also use the approximations to obtain progressively censored sampling plans for log-normal distributed data. These problems illustrate that the presented procedure is highly useful to compute the moments with precision for numerous censoring patterns and, in many cases, is the only valid method because the exact calculation may not be applicable.

Mid –Truncated Burr XII Distribution and Its Applications in Order Statistics

In this paper we define the Mid-Truncated Burr XII distribution and derive some of its statistical properties such as moments, moment generating function, characteristic function, likelihood function, etc. We have also obtained the recurrence relations for single and product moments of order statistics in a random sample of size n drawn from Mid-Truncated Burr XII distribution. Further, the characterization of mid truncated distribution using conditional moments has been given.

On moments of dual generalized order statistics from Topp-Leone distribution

ABSTRACTIn this paper, we have derived exact and explicit expressions for the ratio and inverse moments of dual generalized order statistics from Topp-Leone distribution. This result includes the single and product moments of order statistics and lower records . Further, based on n dual generalized order statistics, we have deduced the expression for Maximum likelihood estimator (MLE) and Uniformly minimum variance unbiased estimator (UMVUE) for the shape parameter of Topp-Leone distribution. Finally, based on order statistics and lower records, a simulation study is being carried out to check the efficiency of these estimators.

Power generalized Weibull distribution based on order statistics

In this article, we establish recurrence relations for the single and product moments of order statistics from the power generalized Weibull (PGW) distribution due to Bagdonovacius and Nikulin (2002). These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we have obtained the means, variances and covariances of order statistics from samples of sizes up to 5 for various values of the shape and scale parameters and present them in figures.

Extended exponential distribution based on order statistics

ABSTRACTThe extended exponential distribution due to Nadarajah and Haghighi (2011) is an alternative to and always provides better fits than the gamma, Weibull, and the exponentiated exponential distributions whenever the data contain zero values. We establish recurrence relations for the single and product moments of order statistics from the extended exponential distribution. These recurrence relations enable computation of the means, variances, and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, and covariances of order statistics and derive best linear unbiased estimates of the extended exponential distribution. Finally, a data application is provided.

Recurrence Relation of Single and Product Moments of Order Statistics from Additive Weibull Distribution

Recurrence Relation of Single and Product Moments of Order Statistics from Additive Weibull Distribution

Exact Moments of order Statistics from The exponentiated Lomax distribution

In this paper, order statistics from the exponentiated Lomax distribution (ELD) are obtained. Exact form for the single, product and Triple moment of order statistics from ELD are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic are presented. Some recurrence relations for the single and product moments of order statistics from ELD are established. Also, the percentage points of single order statistics from ELD are computed.

On some order statistics properties of the Mukherjee-Islam distribution

In this paper, we study the distribution of order statistics of the Mukherjee-Islam distribution. We establish some recurrence relation for single and product moments of order statistics from Mukherjee-Islam distribution. These recurrence relations will enable the computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient recursive manner. The exact analytical expressions of entropy, residual entropy and past residual entropy for order statistics of Mukherjee-Islam distribution are derived.

A skew logistic distribution as an alternative to the model of van Staden and King

ABSTRACTThe logistic distribution is a simple distribution possessing many useful properties and has been used extensively for analyzing growth. Recently, van Staden and King proposed a quantile-based skew logistic distribution. In this paper, we introduce an alternative skew logistic distribution. We then establish recurrence relations for the computation of the single and product moments of order statistics from the standard skew logistic distribution by using the moments of order statistics from the standard half logistic distribution. These enable an efficient computation of means, variances and covariances of order statistics from the skew logistic distibution for all sample sizes. The results become useful in determining the best linear unbiased estimators of the location and scale paramters of the skew logistic distribution. Finally, we provide an example to illustrate the usefulness of the developed model and then compare its fit with that provided by the model of van Staden and King.