Optimal Betting in Casino Blackjack II: Back-Counting

The card counting technique known as ‘back-counting’ is treated analytically. The true count at which the back-counter should optimally enter the game is derived, based on maximising his effective yield. That entry count is found to be in the range of +2 to +3 for a typical 6-deck game, depending on the back-counter's risk profile. If he also adopts an ‘exit’ strategy (abandoning play at a table whose true count has dropped below a lower threshold) and optimises the entry and exit counts simultaneously, he can improve his performance slightly further; the optimal exit count is between ? 2 and ? 3. Because the risk of ruin is very low, he may in addition choose to bet more aggressively than he would if not back-counting—or, conversely, to ‘flat bet’. Criteria are examined for ‘departure’ (abandoning the observation of a table whose true count has yet to reach the entry threshold).     

Order statistics from the linear-exponential distribution,part I: increasing hazard rate case

For the linear-exponential distribution with increasing hazard rate, exact and explicit expressions for means, product moments and percentage points of order statistics are obtained. Some recurrence relations for both single and product moments of order statistics are also derived. These recurrence relations would enable one to obtain all the higher order moments of order statistics for all sample sizes from those of the lower order     

Density estimation using asymmetric kernels and Bayes bandwidths with censored data

We propose a modification to the regular kernel density estimation method that use asymmetric kernels to circumvent the spill over problem for densities with positive support. First a pivoting method is introduced for placement of the data relative to the kernel function. This yields a strongly consistent density estimator that integrates to one for each fixed bandwidth in contrast to most density estimators based on asymmetric kernels proposed in the literature. Then a data-driven Bayesian local bandwidth selection method is presented and lognormal, gamma, Weibull and inverse Gaussian kernels are discussed as useful special cases. Simulation results and a real-data example illustrate the advantages of the new methodology.     

Maximum likelihood estimation of the bimodal failure rate for censored and tied observations

DIMITROV, RACHEV and YAKOVLEV ( 1985 ) have obtained the isotonic maximum likelihood estimator for the bimodal failure rate function. The authors considered only the complete failure time data. The generalization of this estimator for the case of censored and tied observations is now proposed.     

The Incompatibility of Materialism and the Desire for Children: Psychological Insights into the Fertility Discrepancy Among Modern Countries

We examined factors related to attitudes toward marriage and the importance of having children in both the US and Singapore. Path analysis indicated that life dissatisfaction leads to materialism, and both of these factors lead to favorable attitudes toward marriage, which leads to greater desire for children. Further analysis indicated this model was effective in explaining the difference in desire for children between Singaporeans and Americans, whereby Singaporeans have lower life satisfaction, higher materialism, and lower attitudes toward marriage and children. Materialistic standards of success were also related to the emphasis women placed on potential marriage partners’ earning capacity. As Singaporean women had higher materialistic standards, they also placed higher emphasis on potential mates’ earning capacity. Results suggest a consideration of psychological variables such as life satisfaction, materialism, and mate preferences may lead to a better understanding of larger-scale socioeconomic issues, including low fertility rates among developed East Asian countries.     

Catastrophe Risk Models for Evaluating Disaster Risk Reduction Investments in Developing Countries

Major natural disasters in recent years have had high human and economic costs, and triggered record high postdisaster relief from governments and international donors. Given the current economic situation worldwide, selecting the most effective disaster risk reduction (DRR) measures is critical. This is especially the case for low‐ and middle‐income countries, which have suffered disproportionally more economic and human losses from disasters. This article discusses a methodology that makes use of advanced probabilistic catastrophe models to estimate benefits of DRR measures. We apply such newly developed models to generate estimates for hurricane risk on residential structures on the island of St. Lucia, and earthquake risk on residential structures in Istanbul, Turkey, as two illustrative case studies. The costs and economic benefits for selected risk reduction measures are estimated taking account of hazard, exposure, and vulnerability. We conclude by emphasizing the advantages and challenges of catastrophe model‐based cost‐benefit analyses for DRR in developing countries.     

Maximal Invariant and Weakly Equivariant Estimators

Equivariant functions can be useful for constructing of maximal invariant statistic. In this article, we discuss construction of maximal invariants based on a given weakly equivariant function under some additional conditions. The theory easily extends to the case of two or more weakly equivariant functions. Also, we derive a maximal invariant statistic when the group contains a sharply transitive and a characteristic subgroup. Finally, we consider the independence of invariant and weakly equivariant functions under some special conditions.