Bayesian prediction of order statistics with fixed and random sample sizes based on k-record values from Pareto distribution

In this paper, the two-parameter Pareto distribution is considered and the problem of prediction of order statistics from a future sample and that of its geometric mean are discussed. The Bayesian approach is applied to construct predictors based on observed k-record values for the cases when the future sample size is fixed and when it is random. Several Bayesian prediction intervals are derived. Finally, the results of a simulation study and a numerical example are presented for illustrating all the inferential procedures developed here.     

On fiducial generators

Fiducial inference has been gaining presence recently and it is the intention of the present article to look at the notion of fiducial generators; meaning procedures to simulate parameter values that in some sense correspond to simulations from some implicit fiducial distribution. It is well known that when the distribution has group structure, stemming from the natural pivotal associated, a fiducial may be obtained. It is in the non group distributions that there appears to be still room for finding a fiducial distribution. Recently some general procedures have been proposed for dealing with generalized fiducials, but these depend on certain choices for a structural equation or a fiducial equation, as in Hannig (2009 Hannig, J. (2009). On generalized fiducial inference. Stat. Sin. 19:491–544.[Web of Science ®] , [Google Scholar]) or Taraldsen and Lindqvist (2013 Taraldsen, G., Lindqvist, B.H. (2013). Fiducial theory and optimal inference. Ann. Stat. 41(1):323–341.[Crossref], [Web of Science ®] , [Google Scholar]), respectively. A brief presentation is made of an earlier approach to fiducial inference for multivariate parameters, as in Brillinger (1962 Brillinger, D.R. (1962). Examples bearing on the definition of fiducial probability with a bibliography. Ann. Math. Stat. 33(4):1349–1355.[Crossref] , [Google Scholar]), and the implied fiducial generator introduced in Engen and Lillegård (1997 Engen, S., Lillegård, M. (1997). Stochastic simulation conditioned on sufficient statistics. Biometrika 84(1):235–240.[Crossref], [Web of Science ®] , [Google Scholar]), trying to connect them. Three interesting non group distributions are seen; two of them, the truncated exponential and the two-parameter gamma, already reported in literature. A third non group distribution is analyzed; the inverse Gaussian, connecting the fiducial that results following Brillinger (1962 Brillinger, D.R. (1962). Examples bearing on the definition of fiducial probability with a bibliography. Ann. Math. Stat. 33(4):1349–1355.[Crossref] , [Google Scholar]), with a result pertaining confidence limits for the shape parameter in Hsieh (1990 Hsieh, H.K. (1990). Inferences on the coefficient of variation of an inverse-Gaussian distribution. Commun. Stat. - Theory Methods 19(5):1589–1605.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). In the three cases, comparisons are made with the Bayesian posteriors that have been known to be close numerically. Some discussion is made on the issue of singularities of the fiducial density and its connection with densities that do not integrate to unity. As to the case of discrete observables, some comments are made for the Bernoulli distribution, only.     

An optional randomized response model for estimating a rare sensitive attribute using Poisson distribution

The crux of this article is to estimate the mean of the number of persons possessing a rare sensitive attribute based on the Mangat (1991 Mangat, N.S. (1991). An optional randomized response sampling technique using non–stigmatized attribute. Statistica. 51(4):595–602. [Google Scholar]) randomization device by utilizing the Poisson distribution in simple random sampling and stratified sampling. Properties of the proposed randomized response (RR) model have been studied along with recommendations. It is also shown that the proposed model is more efficient than that of Land et al. (2011 Land, M., Singh, S., Sedory, S.A. (2011). Estimation of a rare attribute using Poisson distribution. Statistics. 46(3):351–360.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) in simple random sampling and that of Lee et al. (2013 Lee, G.S., Uhm, D., Kim, J.M. (2013). Estimation of a rare sensitive attribute in stratified sampling using Poisson distribution. Statistics. 47(3):575–589.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) in stratified random sampling when the proportion of persons possessing a rare unrelated attribute is known. Numerical illustrations are also given in support of the present study.     

Slashed generalized Rayleigh distribution

We introduce a new family of distributions suitable for fitting positive data sets with high kurtosis which is called the Slashed Generalized Rayleigh Distribution. This distribution arises as the quotient of two independent random variables, one being a generalized Rayleigh distribution in the numerator and the other a power of the uniform distribution in the denominator. We present properties and carry out estimation of the model parameters by moment and maximum likelihood (ML) methods. Finally, we conduct a small simulation study to evaluate the performance of ML estimators and analyze real data sets to illustrate the usefulness of the new model.     

Gamma-Maxwell distribution

A new two-parameter distribution, the gamma-Maxwell distribution, isproposed and studied. We generate the new distribution using the gamma-G generator of distributions. The proposal distribution can be seen as an extension of the Maxwell distribution with more flexibility in terms of the distribution asymmetry and kurtosis. We study some probability properties, discuss maximum-likelihood estimation and present a real data application indicating that the new distribution can improve the ordinary Maxwell distribution in fitting real data.     

International Migrant Remittances and Labour Supply in Nigeria

The study analyses how remittances to Nigeria affect the labour supply of recipients using Propensity Score Matching (PSM) and a Log‐Linear regression model, with data from the 2013 Nigerian General Household Survey. The PSM results show that for the entire sample, the difference between the average amount of labour supplied per week by those that receive remittances and the amount they would have supplied without remittances is insignificant. The marginal impact analysis also shows that, ceteris paribus, the average labour supply for all recipients is inelastic to remittances. The results from the sub‐group analysis, however, show that receiving remittances negatively affects the labour supply of the self‐employed in agriculture, teenagers and the elderly. These results led us to the recommendation that policies to increase the inflow of remittances should be encouraged but in tandem with programmes to educate farmers on the benefit of investing remittances received in their farming business.     

Residential Remittances and Food Security in the Upper West Region of Ghana

In recent years, out migration from the Upper West Region to the southern belt of Ghana for farming has become commonplace. The natural question that has arisen is: what is the potential impact of remittances from this migration pattern on food security in the region? Using multivariate ordered logistic regression this study assesses the linkage between remittances and household food security (derived using the HFIAS) among urban and rural households (n=1,438) in the region. The findings show that urban remittance‐receiving households and rural remittance and non‐remittance receiving households were more likely (OR=2.44, p<0.05; OR=2.46, p<0.001; and OR=1.49, p<0.1, respectively) to report being more severely food‐insecure than urban non‐remittance receiving households. The findings demonstrate that household strategies such as migration and remittances on their own are not sufficient to ameliorate the precarious food insecurity situation of the region. The study calls for development of alternative livelihoods in the region.     

Do Some Students Need Special Protection From Research on Sex and Trauma? New Evidence for Young Adult Resilience in “Sensitive Topics” Research

Institutional review boards (IRBs) have expressed concerns that certain individuals or groups, such as participants who are younger, ethnic minorities, or who have certain psychological or personality traits, may be particularly distressed when participating in “sensitive topics” research. This study examined the effects of several demographic and individual difference factors (i.e., age, sex, ethnicity, religiosity, Big Five personality traits, and baseline psychological distress levels) on reactions to participation in sensitive topics research. Participants were 504 undergraduates who completed an extensive battery of either trauma/sex questionnaires or cognitive tests and rated their positive and negative emotional reactions and the perceived benefits and mental costs of participating. They also compared research participation to normal life stressors. Our findings indicated that individual difference and demographic risk factors do not increase participant distress after participating in sex/trauma research over and above that experienced after participating in traditionally minimal-risk cognitive tasks. Participants generally found research participation less distressing than normal life stressors and even enjoyable.