Estimation of parameters of a pareto distribution by generalized order statistics

In this paper we address the problem of estimating the parameters of Pareto II distribution based on generalized order statistics. The estimators based on order statistics and record values are shown to be special cases of these estimators.     

Asymptotic Behavior of the Hazard Rate Kernel Estimator Under Truncated and Censored Data

In this article, we give the asymptotic mean integrated squared error and the mean squared error for the kernel estimator of the hazard rate from truncated and censored data. Martingale techniques and combinatory calculus are used to obtain these results. A probability bound and the optimal bandwidth choice are also given.     

Inference for the generalized Rayleigh distribution based on progressively censored data

In this paper, and based on a progressive type-II censored sample from the generalized Rayleigh (GR) distribution, we consider the problem of estimating the model parameters and predicting the unobserved removed data. Maximum likelihood and Bayesian approaches are used to estimate the scale and shape parameters. The Gibbs and Metropolis samplers are used to predict the life lengths of the removed units in multiple stages of the progressively censored sample. Artificial and real data analyses have been performed for illustrative purposes.     

Health Divide: Economic and Demographic Factors Associated with Self-Reported Health Among Older Malaysians

Data from the 2004 Survey of Economic and Financial Aspects of Aging in Malaysia were analyzed to determine factors associated with self-reported health status among older Malaysians. Odds of self-reporting health as bad versus moderate or good were higher for respondents who were in lower income quintiles, who perceived their financial situation as bad, who were older and who were not married. Malay, Chinese, Indian, and Bumiputra ethnic groups had lower odds of perceiving their health to be bad as compared with those in other ethnic groups.     

Moments of Order Statistics from Weibull Distribution in the Presence of Multiple Outliers

In this article, we derive exact expressions for the single and product moments of order statistics from Weibull distribution under the contamination model. We assume that X₁, X₂, …, X_{n ? p} are independent with density function f(x) while the remaining, p observations (outliers) X_{n ? p + 1}, …, X_n are independent with density function arises from some modified version of f(x), which is called g(x), in which the location and/or scale parameters have been shifted in value. Next, we investigate the effect of the outliers on the BLUE of the scale parameter. Finally, we deduce some special cases.     

The photo‐survey research method: capturing life in the city

Recent promotion of city centre living within UK policy has led to a commensurate interest in city centre conditions and the opinions and experiences of the people who live there. An apposite, straightforward method to capture city centre residents' experiences and views is described in this article. We successfully combined a novel, under‐utilized visual technique (self‐directed photography) with qualitative methods (log‐sheets and interviews) in the form of a ‘photo‐survey’. A background to visual methodologies is presented in this article, alongside a critique of using the photo‐survey with 84 city centre residents to investigate environmental conditions and perceptions within three of the UK's major cities. The method provided a rich, detailed set of data, but also brought a number of noticeable benefits to the data collection process. The photo‐survey not only effectively captured and documented life in the city but also acted as an ‘agent for change’, evoking thoughts and feelings which ultimately encouraged participants to reflect on their existing perceptions and urban experiences. The study also raises some important considerations for future work undertaken with this method and with using photographs as a set of data, and proposes techniques for minimising potential problems.     

Trends in reproductive behavior among young single women in Colombia and Peru: 1985–1999

Using "calendar" data for single women aged 15-24 from successive Demographic and Health Surveys (DHS) conducted in Colombia and Peru during the 1990s, we document trends, year by year, in sexual activity, the use of contraceptives, and subsequent reproductive outcomes. We provide evidence of the important and hitherto largely untapped potential of DHS calendar data to draw complete sexual and reproductive profiles when data from various surveys are integrated. Over the period 1985-1999, young single women in both Colombia and Peru became sexually active at younger ages. The use of contraceptives, especially the use of condoms, increased but did not fully offset the rise in sexual activity, and thus the incidence of premarital conceptions rose among young single women. In both countries, sharp declines occurred in the proportion of premaritally conceived births that were reported as being wanted.     

Analysis of incomplete durations with application to contraceptive use

Models for analysing incomplete durations obtained from cross-sectional surveys are presented. The aim of the paper is to develop a framework for analysing the incomplete duration of episodes in progress at the time of the survey by formulating generalized linear models and fitting and assessing them by using standard statistical packages. The maximum quasi-likelihood method is used for model fitting. The choice of the distribution and the diagnostic procedures are discussed. Simulated data from two distributions (the Weibull and log-logistic distributions) are used to evaluate the methodology developed and to assess model misspecifications. A data set on the current use of the contraceptive pill from a cross-sectional survey in Egypt is analysed.     

Projection‐Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments

It is well known that standard asymptotic theory is not applicable or is very unreliable in models with identification problems or weak instruments. One possible way out consists of using a variant of the Anderson–Rubin ((1949), AR) procedure. The latter allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, but not for individual coefficients. This problem may in principle be overcome by using projection methods (Dufour (1997), Dufour and Jasiak (2001)). At first sight, however, this technique requires the application of costly numerical algorithms. In this paper, we give a general necessary and sufficient condition that allows one to check whether an AR‐type confidence set is bounded. Furthermore, we provide an analytic solution to the problem of building projection‐based confidence sets from AR‐type confidence sets. The latter involves the geometric properties of “quadrics” and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are needed to build the confidence intervals.