Covariances Of Order Statistics Research Articles

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.

Estimation with Modified Power Function Distribution Based on Order Statistics with Application to Evaporation Data

The modified power function distribution is an important distribution for analyzing the lifetime data, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub shaped failure rate. In this paper, we derive the exact explicit expressions for the single and double (product) of order statistics from the modified power function distribution. By using these relations, we have tabulated the expected values, second moments, variances and covariances of order statistics from samples of sizes up to 10 for various values of the parameters. Also, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on Type-II right-censored samples. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to one real data set.

Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application

The generalized Lindley distribution is an important distribution for analyzing the stress–strength reliability models and lifetime data, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub shaped failure rate. In this paper, we derive the exact explicit expressions for the single, double (product), triple and quadruple moments of order statistics from the generalized Lindley distribution. By using these relations, we have tabulated the expected values, second moments, variances and covariances of order statistics from samples of sizes up to 10 for various values of the parameters. Also, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on Type-II right-censored samples. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to some real data set.

Order Statistics from the Power Lindley Distribution and Associated Inference with Application

Power Lindley distribution has been proposed recently by Ghitany et al. (Comput Stat Data Anal 64:20–33, 2013) as a simple and useful reliability model for analysing lifetime data. This model provides more flexibility than the Lindley distribution in terms of the shape of the density and hazard rate functions as well as its skewness and kurtosis. For this distribution, exact explicit expressions for single moments, product moments, marginal moment generating functions and joint moment generating functions of each of these order statistics are derived. By using these relations, we have tabulated the expected values, second moments, variances and covariances of order statistics from samples of sizes up to 10 for various values of the parameters. In addition, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on Type-II right-censored samples. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to some real data set.

Relations for Moments of Generalized Order Statistics from Extended Exponential Distribution

SYNOPTIC ABSTRACTThe extended exponential distribution due to Nadarajah and Haghighi (2011) is an alternative, and always provides better fits than the gamma, Weibull, and the generalized exponential distributions whenever the data contains zero values. In this article, we consider the generalized order statistics (GOS) from this distribution. We obtain exact explicit expressions as well as recurrence relations for the single, product, and conditional moments of generalized order statistics from the extended exponential (EE) distribution. Then, we use these results to compute the means, variances, and covariances of order statistics and record values for samples of different sizes for various values of the shape and scale parameters. Further, we compute the mean and variances for progressively Type II censored order statistics.

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.

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.

Application of Concomitants of Order Statistics of Independent Non Identically Distributed Random Variables in Estimation

In this article, we obtain expressions for the pdf of a single concomitant of order statistic and the joint pdf of a pair of concomitants of order statistics of independent non identically distributed random variables. Using these expressions, we find the means, variances and covariances of order statistics arising from independent non identically distributed bivariate Pareto distributions. A method of estimation of a common parameter involved in several bivariate Pareto distributions using concomitants of order statistics is also discussed.

Recursive computation of the single and product moments of order statistics from the complementary exponential–geometric distribution

The complementary exponential–geometric distribution has been proposed recently as a simple and useful reliability model for analysing lifetime data. For this distribution, some recurrence relations are established for the single and product moments of order statistics. These recurrence relations enable the computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient recursive manner. By using these relations, we have tabulated the means, variances and covariances of order statistics from samples of sizes up to 10 for various values of the shape parameter θ. These values are in turn used to determine the best linear unbiased estimator of the scale parameter β based on complete and Type-II right-censored samples.

Generalized secant hyperbolic order statistics and associated inferences

In this article, we consider the generalized secant hyperbolic (GSH) distribution with known shape parameter t. Exact expressions for single and product moments of order statistics are established. The expressions are represented in terms of Riemann zeta, polygamma and hypergeometric functions. These special functions allow us to use a series of Mathematica procedures that will compute the means, variances and covariances of order statistics from the GSH distribution. The so-obtained values are used to compute the coefficients of the best linear unbiased estimators of the location and scale parameters. The variances of these estimators are also presented. A real data set has been performed to illustrate our findings.

Series approximations for moments of order statistics using MAPLE

In this paper, we present a series of Maple procedures that will approximate the means, variances, and covariances of order statistics from any continuous population using series approximations in the form of David and Johnson's (Biometrika 41 (1954) 228–240) approximation. These procedures will allow one to improve upon the accuracy of David and Johnson's approximation by extending the series to include higher order terms.

Estimation of the location and scale parameters of generalized exponential distribution based on order statistics

In this paper we consider the generalized exponential distribution with known shape parameter Θ. We first derive the exact forms of means, variances and covariances of order statistics. We use these expressions in obtaining the necessary coefficients for the best linear unbiased estimators of the location and scale parameters for Θ=0.5(0.5)5.0 and for sample sizes up to ten. The variances and covariances of these estimators are also given.

Extended tables for the moments of gamma-distribution order statistics

The authors tabulate expectations, variances, and covariances of order statistics from a sample of size n from a standard gamma distribution with shape parameter r. The expected values are n=1(1)10(5)40 and r =5(1)8; the covariances are n=15(5)25 and r=2(1)5.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Expected values, variances and covariances of order statistics for student's t-distribution with two degrees of freedom

Formulae for computing the exact values of the expected values, variances and covariances of the order statistics of random samples of size n from a distribution related to the Student's t-distribution with two degrees of freedom are developed. Tables of these values for n[d] 20, accurate to ±0.5 × 10-9are given.

Computation of variances and covariances of order statistics from the geometric distribution

An explicit expression for the expected value of the product of two order statistics from the geometric distribution is derived. A method of computation of the expected values and covariances of order statistics is discussed. Computational errors are avoided by use of integer mode arithmetic.

Asymptotic calculations of functions of expected values and covariances of order statistics

AbstractSuppose m and V are respectively the vector of expected values and the covariance matrix of the order statistics of a sample of size n from a continuous distribution F. A method is presented to calculate asymptotic values of functions of m and V–1, for distributions F which are sufficiently regular. Values are given for the normal, logistic, and extreme‐value distributions; also, for completeness, for the uniform and exponential distributions, although for these other methods must be used.

A relation for the covariances of order statistics from n independent and non-identically distributed random variables

We derive a simple relation satisfied by the covariances of order statistics in the i.i.d. case and then generalize it to the case when the variables are independent and non-identically distributed. This relation could be employed successfully either to check the calculations or to reduce the amount of direct computations involved in evaluating the covariances of order statistics from an outlier model.

Order statistics from the type i generalized logistic distribution

In this paper, we first obtain three generalized forms of the standard logistic distribution. These are derived by compounding an extreme-value distribution of the doubly exponential type, a reduced log-Weibull distribution and an exponential-gamma distribution, respectively, with a gamma distribution. The usefulness of these three types of generalized logistic distributions in some estimation problems, and also in some robustness studies, is pointed out. Finally, we study the order statistics from the Type I generalized logistic distribution in detail. We derive exact and explicit expressions for the means, variances and covariances of order statistics in terms of the gama function and its successive derivatives. Percentage points and modes of order statistics are also discussed

Variances and Covariances of Order Statistics from the Gamma Distribution

Variances and Covariances of Order Statistics from the Gamma Distribution

Variances and covariances of order statistics from the gamma distribution

SUMMARY The expectations, variances and covariances of the order statistics in a sample of size n from a standardized gamma distribution with parameter r are tabulated for r = 2(1)5 and n = 2(1)10.