Prediction of order statistics and record values based on ordered ranked set sampling

In this paper, we consider two-sample prediction problems. First, based on ordered ranked set sampling (ORSS) introduced by Balakrishnan and Li [Ordered ranked set samples and applications to inference. Ann Inst Statist Math. 2006;58:757–777], we obtain prediction intervals for order statistics from a future sample and compare the results with the one based on the usual-order statistics. Next, we construct prediction intervals for record values from a future sequence based on ORSS and compare the results with the one based on an another independent record sequence developed recently by Ahmadi and Balakrishnan [Prediction of order statistics and record values from two independent sequences. Statistics. 2010;44:417–430].     

A New Adaptive Variable Sample Size Approach in EWMA Control Chart

Adaptive control charts have been developed for improving the capability of control charts in detecting small shifts. In this article, we propose a new exponential weighted moving average control chart with variable sample size, in which the sample size is determined as an integer linear function by EWMA statistic value. The performance of the proposed VSS EWMA control chart is compared with FSS EWMA as well as traditional VSS EWMA control charts. The results show the better performance of the proposed VSS strategy respect to the traditional one and fixed sample size.     

The effect of fat-tailed error terms on the properties of systemwise RESET test

The small sample properties of the systemwise RESET (Regression Specification Error Test) test for functional misspecification are investigated using normal and non-normal error terms. When using normally distributed or less heavy tailed error terms, we find the Rao's multivariate F-test to be best among all other alternative test methods (i.e. Wald, Lagrange Multiplier and Likelihood Ratio). Using the bootstrap critical values, however, all test methods perform satisfactorily in almost all situations. However, the test methods perform extremely badly (even the RAO test) when the error terms are very heavy tailed.     

A case study of urban ecological networks and a sustainable city: Tehran’s metropolitan area

The aim of this study is to propose the application of landscape ecology in planning urban ecological networks to conserve nature in urban landscapes and to develop a sustainable use of urban lands. Compared to the classical planning approach based on socio-economic land suitability, the principles of landscape ecology are helpful simultaneously conserving the ecological processes of landscapes and their steady changes. This approach could help in defining sustainable landscape development, aiming for a balance between both physical and natural systems in urban areas. This research is focused on the ecological networks in Tehran’s metropolitan area as a case study to provide a model for network planning in other urban areas, where urbanization seriously threats the natural environment. In concluding this research, the spatial structure and function of the area are studied and categorized based on the patch-corridor-matrix model. The paper concludes with methods of intervention and suggestions for the structural and functional improvement of urban landscapes towards achieving a more sustainable form of land use planning.     

On simulating truncated skewed Cauchy random variables

Shirvani and Soltani suggested a method for characterizing and simulating one-sided truncated Cauchy random variables. For simulation, that involves solving a nonlinear transformation in each iteration. Here, we propose an alternative method to generate Cauchy random variables. Our method is more general (e.g., incorporates one-sided and two-sided truncations) and does not involve solving any equation. It can be implemented even using a hand calculator.     

Estimation with the lognormal distribution on the basis of records

Record scheme is a method to reduce the total time on test of an experiment. In this scheme, items are sequentially observed and only values smaller than all previous ones are recorded. In some situations, when the experiments are time-consuming and sometimes the items are lost during the experiment, the record scheme dominates the usual random sample scheme [M. Doostparast and N. Balakrishnan, Optimal sample size for record data and associated cost analysis for exponential distribution, J. Statist. Comput. Simul. 80(12) (2010), pp. 1389–1401]. Estimation of the mean of an exponential distribution based on record data has been treated by Samaniego and Whitaker [On estimating population characteristics from record breaking observations I. Parametric results, Naval Res. Logist. Q. 33 (1986), pp. 531–543] and Doostparast [A note on estimation based on record data, Metrika 69 (2009), pp. 69–80]. The lognormal distribution is used in a wide range of applications when the multiplicative scale is appropriate and the log-transformation removes the skew and brings about symmetry of the data distribution [N.T. Longford, Inference with the lognormal distribution, J. Statist. Plann. Inference 139 (2009), pp. 2329–2340]. In this paper, point estimates as well as confidence intervals for the unknown parameters are obtained. This will also be addressed by the Bayesian point of view. To carry out the performance of the estimators obtained, a simulation study is conducted. For illustration proposes, a real data set, due to Lawless [Statistical Models and Methods for Lifetime Data, 2nd ed., John Wiley & Sons, New York, 2003], is analysed using the procedures obtained.     

Some results on conditional expectations of lower record values

In this paper, we propose a measure for obtaining the expectation of time between two lower k-records under the condition that the greater one is given. Several properties of the proposed measure are derived. Some characterization results and stochastic comparisons based on the new measure are also provided.     

On characterizations of the generalized Pareto distributions based on progressively censored order statistics

It is well-known, in the literature, that most of the characterization results on exponential distribution are based on the solution of Cauchy functional equation and integrated Cauchy functional equation. In the present paper, we consider the functional equation $$F(x) = F(xy) + F(xQ(y)), \quad x, xQ(y) \in [0, \theta),\; y \in [0,1],$$ where F and Q satisfy certain conditions, to give some new characterization results on the generalized Pareto distributions based on progressively Type-II right censored order statistics. We prove the main results without restricting to distributions that are absolutely continuous with respect to Lebesgue measure.     

The odd power cauchy family of distributions: properties,regression models and applications

We study some mathematical properties of a new generator of continuous distributions with one extra parameter called the odd power Cauchy family including asymptotics, linear representation, moments, quantile and generating functions, entropies, order statistics and extreme values. We introduce two bivariate extensions of the new family. The maximum likelihood method is discussed to estimate the model parameters by means of a Monte Carlo simulation study. We define a new log-odd power Cauchy–Weibull regression model. The usefulness of the proposed models is proved empirically by means of three real data sets.