In this work the ranked set sampling technique has been applied to estimate the scale parameter
of a log-logistic distribution under a situation where the units in a sample can be ordered by judgement method without any error. We have evaluated the Fisher information contained in the order statistics arising from this distribution and observed that median of a random sample contains the maximum information about the parameter
. Accordingly we have used median ranked set sampling to estimate
. We have further carried out the multistage median ranked set sampling to estimate
with improved precision. Suppose it is not possible to rank the units in a sample according to judgement method without error but the units can be ordered based on an auxiliary variable
such that
(X, Z)
has a Morgenstern type bivariate log-logistic distribution (MTBLLD). In such a situation we have derived the Fisher information contained in the concomitant of rth order statistic of a random sample of size
from MTBLLD and identified those concomitants among others which possess largest amount of Fisher information and defined an unbalanced ranked set sampling utilizing those units in the sample and thereby proposed an estimator of
using the measurements made on those units in this ranked set sample.
Related Content
Inference of R=P[X
This paper deals with the estimation of R=P when X and Y come from two independent generalized logistic distributions with different parameters. The maximum-likelihood estimator (MLE) and its asymptotic distribution are proposed. The asymptotic distribution is used to construct an asymptotic conf...

Estimation of the stress–strength reliability for the generalized logistic distribution
Ragab (Microelectronics Reliability, 91–95, 31, 1991) described the Bayesian and empirical Bayesian methods for estimation of the stress–strength parameter R = P ( Y < X ) , when X and Y are independent random variables from two generalized logistic (GL) distributions having the...
Semiparametric estimation of a mixture of two linear regressions in which one component is known
A new estimation method for the two-component mixture model introduced inVandekerkhove (2012) is proposed. This model, which consists of a two-componentmixture of linear regressions in which one component is entirely known whilethe proportion, the slope, the intercept and the error distribution o...

Automatic smoothing parameter selection in GAMLSS with an application to centile estimation
A method for automatic selection of the smoothing parameters in a generalised additive model for location, scale and shape (GAMLSS) model is introduced. The method uses a P-spline representation of the smoothing terms to express them as random effect terms with an internal (or local) maximum like...
On the likelihood estimation of the parameters of Gompertz distribution based on complete and progressively Type-II censored samples
In this paper, by considering a progressively Type-II censored sample from the two-parameter Gompertz distribution, a necessary and sufficient condition is established for the existence and uniqueness of the maximum-likelihood estimates of the shape and scale parameters. The results for the speci...

The beta generalized logistic distribution
For the first time, a four-parameter beta generalized logistic distribution is obtained by compounding the beta and generalized logistic distributions. The new model extends some well-known distributions and its shape is quite flexible, specially the skewness and the tail weights, due to the extr...
Variable selection in joint location and scale models of the skew-normal distribution
We propose a unified penalized likelihood method which can simultaneously select significant variables in the location and scale models. Furthermore, the proposed variable selection method can simultaneously perform parameter estimation and variable selection in the location and scale models. Wit...

Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector
We consider estimation of the mean vector, $theta $, of a spherically symmetric distribution with known scale parameter under quadratic loss and when a residual vector is available. We show minimaxity of generalized Bayes estimators corresponding to superharmonic priors with a non decreasing Lapl...
Parameter Interpretation in Skewed Logistic Regression with Random Intercept
This paper aims at providing the prior and posterior interpretations for the parameters in the logistic regression model with random or cluster-level intercept when univariate and multivariate classes of skew normal distributions are assumed to model the random effects behavior. We obtain the pri...

Optimal Rates of Convergence of Transelliptical Component Analysis
Han and Liu (2012) proposed a method named transelliptical component analysis(TCA) for conducting scale-invariant principal component analysis on highdimensional data with transelliptical distributions. The transelliptical familyassumes that the data follow an elliptical distribution after unspec...