A comparison of estimation techniques for the three parameter pareto distribution

This paper compares minimum distance estimation with best linear unbiased estimation to determine which technique provides the most accurate estimates for location and scale parameters as applied to the three parameter Pareto distribution. Two minimum distance estimators are developed for each of the three distance measures used (Kolmogorov, Cramer‐von Mises, and Anderson‐Darling) resulting in six new estimators. For a given sample size 6 or 18 and shape parameter 1(1)4, the location and scale parameters are estimated. A Monte Carlo technique is used to generate the sample sets. The best linear unbiased estimator and the six minimum distance estimators provide parameter estimates based on each sample set. These estimates are compared using mean square error as the evaluation tool. Results show that the best linear unbaised estimator provided more accurate estimates of location and scale than did the minimum estimators tested.     

Estimation of Measures in M/M/1 Queue

Maximum likelihood and uniform minimum variance unbiased estimators of steady-state probability distribution of system size, probability of at least ? customers in the system in steady state, and certain steady-state measures of effectiveness in the M/M/1 queue are obtained/derived based on observations on X, the number of customer arrivals during a service time. The estimators are compared using Asympotic Expected Deficiency (AED) criterion leading to recommendation of uniform minimum variance unbiased estimators over maximum likelihood estimators for some measures.     

Two‐generation preschool programme: immediate and 7‐year‐old outcomes for low‐income children and their parents

Preschool children living in low‐income families are at increased risk for poor outcomes; early intervention programmes mitigate these risks. While there is considerable evidence of the effectiveness of centre‐based programmes in other jurisdictions, there is limited research about Canadian programmes, specifically programmes that include children and parents. The purpose of this study was to evaluate a single‐site, two‐generation preschool demonstration programme for low‐income families in Canada. A single group, pre‐test (programme intake) /post‐test (programme exit) design with a 7‐year‐old follow‐up was used. Between intake and exit, significant improvements in receptive language and global development were found among the children, and significant improvements in self‐esteem, use of community resources, parenting stress and risk for child maltreatment were found among the parents. These positive improvements were sustained until the children were 7 years old. Public investment in two‐generation preschool programmes may mitigate risks for suboptimal child development and improve parental psychosocial outcomes.     

Problem structuring methods as intervention tools: Reflections from their use with multi-organisational teams

Problem structuring methods (PSMs), also known as soft OR approaches, are most commonly employed with teams formed by members who tend to operate within an overall framework of authority and accountability, and most of whom have the ‘power to act’ on their recommendations. However, other PSM users include teams whose members are drawn from different organisational settings to work on a problem of common interest. The multi-organisational nature of such multi-organisational teams (MOTs) adds further complexity to the PSM modelling and facilitation processes by increasing the potential for conflict regarding the problem. In addition, members of MOTs tend not to operate within an overall framework of authority and accountability and, therefore, do not necessarily have full authority to commit themselves to their joint agreements. This paper reports on the design and application of a PSM-based methodology with three such groups, within the context of a multi-organisational collaboration in the UK construction industry. The paper reflects on the apparent success of the intervention, discusses the appropriateness of PSMs in this particular intervention context, as well as the generalisibility of the findings to other PSMs and/or multi-organisational contexts. Directions for the research and practice of PSMs with MOTs are also presented.     

Examining the impact of family services on homeless children

This study examined the impact on children of services delivered through a collaborative initiative designed to provide supports to working poor families who are homeless or at immediate risk of becoming homeless. Overall, a number of positive findings can serve to inform the development of promising intervention strategies for children in homeless families and highlight areas for further research. Along with improved housing status, there was a statistically significant improvement in the economic self‐sufficiency of the families served, regardless of whether they completed the full programme cycle. In addition, youth self‐report data indicated significant improvements in externalizing and internalizing behaviour. The ability to combine programme data with school data for participating children also made it possible to explore school performance outcomes. Although these results did not indicate a change in participants’ levels of attendance or reading performance, there was a statistically significant improvement in students’ math scores. Moreover, when participating children were compared with a group of students matched on their level of academic performance at baseline who had not received housing or homeless services, no significant differences were detected between groups post‐intervention, indicating that services may help reduce the risk of homeless students’ falling further behind their peers academically.     

新型社会救助制度:成就、问题与发展方向

１９７８年以来,中国初步建立了以最低生活保障制度、医疗救助制度、五保供养制度为主要内容的新型社会救助制度体系,社会救助覆盖面不断扩大、救助力度不断增强、法律建设取得了较快发展。然而,中国新型社会救助还存在救助理念滞后、二元分割现象明显、责任分担机制不合理、待遇调整机制不科学、对象瞄准机制不健全等问题。研究认为:新型社会救助制度的发展方向是确立积极的社会救助理念、统筹城乡社会救助发展、完善瞄准机制、建立合理的待遇调整机制。     

Comparison of point estimators of normal percentiles

There are available several point estimators of the percentiles of a normal distribution with both mean and variance unknown. Consequently, it would seem appropriate to make a comparison among the estimators through some “closeness to the true value” criteria. Along these lines, the concept of Pitman-closeness efficiency is introduced. Essentially, when comparing two estimators, the Pit-man-closeness efficiency gives the “odds” in favor of one of the estimators being closer to the true value than is the other in a given situation. Through the use of Pitman-closeness efficiency, this paper compares (a) the maximum likelihood estimator, (b) the minimum variance unbiased estimator, (c) the best invariant estimator, and (d) the median unbiased estimator within a class of estimators which includes (a), (b), and (c). Mean squared efficiency is also discussed.     

Alternative parameter estimators based upon grouped data

The problem of estimating population parameters based upon grouped data is considered and several alternative estimation schemes such as the method of scoring, least lines, least squares, minimum chi square, and a method of approximating method of moments and maximum likelihood estimators are considered. These estimators are compared with maximum likelihood and method of moments estimators based upon individual observations using a Monte Carlo study where the parent population is characterized by a gamma distribution. An application of these techniques to fitting a gamma distribution to 1970-74 census income data is considered.     

On the umvu estimators after using a normalizing transformation

The conditional distribution given complete sufficient statistics is used along with the Rao-Blackwell theorem to obtain uniformly minimum variance unbiased (UMVU) estimators after a transformation to normality has been applied to data. The estimators considered are for the mean, the variance and the cumulative distribution of the original non-normal data. Previous procedures to obtain UMVU estimators have used Laplace transforms, Taylor expansions and the jackknife. An integration method developed in this paper requires only integrability of the normalizing transformation function. This method is easy to employ and it is always possible to obtain a numerical result.     

A unified approach to minimum variance unbiased estimation of a probability function belonging to an exponential family

The problem of minimum variance unbiased estimation of the probability density function of a random variable belonging to an exponential family is considered. The method of estimation proposed in this paper requires the solution of a certain integral equation. For many probability distributions the solution of this equation is given by a known result in integral transform theory.