摘要 :
In some quarters, especially beginners learning statistics and probability, one generally accepts a claim such as a chi(2)(1) random variable (rv) must be the square of a standard normal rv or a F-1,F-1 rv must be the square of a ...
展开
In some quarters, especially beginners learning statistics and probability, one generally accepts a claim such as a chi(2)(1) random variable (rv) must be the square of a standard normal rv or a F-1,F-1 rv must be the square of a Student's t(1) rv. This feeds into more misconceptions later. Hence, we begin with a brief but general construct and then illustrate a number of rvs explicitly which are drastically different from a standard normal or Student's t(1) rv whose squares are distributed as chi(2)(1) or F-1,F-1 respectively. This simply presented note reinforces basic understanding of lessons in such core topics covered in classrooms for both undergraduate and graduate students.
收起
摘要 :
The main idea of this paper is to present families of bivariate distributions that depend in their formation on adding a shape parameter to the powers of the hazard and reversed hazard functions in different manners, which would p...
展开
The main idea of this paper is to present families of bivariate distributions that depend in their formation on adding a shape parameter to the powers of the hazard and reversed hazard functions in different manners, which would provide additional flexibility in applications. Different baseline distributions were used namely, exponential, inverse exponential, uniform, inverse uniform, inverse Ray-leigh, Gompertz and Pareto. Many of the mathematical properties of these families are discussed in detail. Moreover, it is observed that the new bivariate distributions also can make appropriate modeling of three real data sets.
收起
摘要 :
If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when g and G are...
展开
If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when g and G are taken to come from one of Laplace, logistic, Student’s t, uniform, exponential power or the Bessel function distribution.
收起
摘要 :
Log-concave random variables and their various properties play an increasingly important role in probability, statistics, and other fields. For a distribution F, denote by D-F, the set of distributions G such that the convolution ...
展开
Log-concave random variables and their various properties play an increasingly important role in probability, statistics, and other fields. For a distribution F, denote by D-F, the set of distributions G such that the convolution of F and G has a log-concave probability mass function or probability density function. In this paper, we investigate sufficient and necessary conditions under which D-F subset of D-G, where F and G belong to a parametric family of distributions. Both discrete and continuous settings are considered.
收起
摘要 :
Dodge and Rousson (1999) and Zhang (2007) gave an expression for Cov(X, S2) based upon independent and identically distributed (i.i.d.) observations not necessarily normal. In this note, we derive the expression (Theorem 2.1) for ...
展开
Dodge and Rousson (1999) and Zhang (2007) gave an expression for Cov(X, S2) based upon independent and identically distributed (i.i.d.) observations not necessarily normal. In this note, we derive the expression (Theorem 2.1) for Cov(X, S2) based upon non-independent and/or nonidentically distributed observations and move away from the i.i.d. scenario. Some illustrations are included.
收起
摘要 :
A new distribution is proposed for modeling lifetime data. It has better hazard rate properties than the gamma, lognormal and the Weibull distributions. A comprehensive account of the mathematical properties of the new distributio...
展开
A new distribution is proposed for modeling lifetime data. It has better hazard rate properties than the gamma, lognormal and the Weibull distributions. A comprehensive account of the mathematical properties of the new distribution including estimation and simulation issues is presented. A real data example is discussed to illustrate its applicability.
收起
摘要 :
It may sometimes be desirable to introduce bounds into probability distributions to formalise the presence of upper or lower physical limits to data to which the distribution has been applied. For example, an upper bound in raindr...
展开
It may sometimes be desirable to introduce bounds into probability distributions to formalise the presence of upper or lower physical limits to data to which the distribution has been applied. For example, an upper bound in raindrop sizes might be represented by introducing an upper bound to an exponential drop-size distribution. However, the standard method of truncating unbounded probability distributions yields distributions with non-zero probability density at the resulting bounds. In reality it is likely that physical bounding processes in nature increase in intensity as the bound is approached, causing a progressive decline in observation relative frequency to zero at the bound. Truncation below a y-axis point is proposed as a simple alternative means of creating more natural truncated probability distributions for application to data of this type. The resulting "y-truncated" distributions have similarities with the traditional truncated distributions but probability densities have the desirable feature of always declining to zero at the bounds. In addition, the y-truncation approach can also serve in its own right as a means of creating a rich new class of bounded probability distributions when transformations of y-truncated distributions are included.
收起
摘要 :
An implicit distribution resembles a posterior distribution of θ in the presence of a specific prior distribution on θ. But, then it is not clear if anything additional or distinctly novel is achieved via implicit distributions ...
展开
An implicit distribution resembles a posterior distribution of θ in the presence of a specific prior distribution on θ. But, then it is not clear if anything additional or distinctly novel is achieved via implicit distributions that goes above and beyond what is achieved through usual full-blown Bayesian analyses. On the other hand, an implicit distribution resembles a fiducial distribution of θ when no specific prior distribution is assumed for θ. In that case, however, it seems fair to criticize an implicit distribution along the lines of well-documented criticisms and controversies that surround Fisher's fiducial distribution even today, nearly 75 years after Fisher (1930) first introduced the concept. Any intrinsic value of implicit distributions remains unclear in my view.
收起
摘要 :
Insecticide-treated nets are a key intervention for malaria prevention. While mass distribution can rapidly scale up ITN coverage, multiple channels may be needed to sustain high levels of ITN access and ownership. In Ghana’s Eas...
展开
Insecticide-treated nets are a key intervention for malaria prevention. While mass distribution can rapidly scale up ITN coverage, multiple channels may be needed to sustain high levels of ITN access and ownership. In Ghana’s Eastern Region, a continuous ITN distribution pilot, started in October 2012, 18–24?months after a mass campaign. The pilot distributed ITNs through antenatal care services (ANC), child welfare clinic services (CWC) through the Expanded Programme on Immunization, and to students in two classes of primary schools. ITN ownership and access were evaluated through two cross-sectional surveys, conducted at baseline in April 2012, 11–15?months after the mass campaign, and at endline in December 2013, after 1?year of continuous distribution. A representative sample was obtained using a multi-stage cluster sampling design. Household heads were interviewed using a structured questionnaire. Household ownership of at least one ITN was 91.3% (95% CI 88.8–93.9) at baseline and was not statistically significant at endline 18?months later at 88.3% (95% CI 84.9–91.0) (p?=?0.10). Ownership of at least 1 ITN per two people significantly decreased from 51.3% (95% CI 47.1–55.4) to 40.2% (95% CI 36.4–44.6) (p?<?0.01). Population access to an ITN within the household also significantly decreased from 74.5% (95% CI 71.2–77.7) at baseline to 66.4% (95% CI 62.9–69.9) at endline (p?<?0.01). The concentration index score for any CD channel was slightly positive (0.10; 95% CI 0.04–0.15). Thirty-one months after the mass campaign, the 15?months of continuous distribution activities had maintained levels of household ownership at least one ITN, but household ownership of one ITN for every two people and population access to ITN had declined. Ownership and access were higher with the CD programme than without. However, the number of ITNs delivered via ANC, CWC and two primary school classes were insufficient to sustain coverage targets. Future programmes should implement continuous distribution strategies fully within 1?year after a campaign or widen eligibility criteria (such as increase the number of classes) during the first year of implementation to make up for programme delays.
收起
摘要 :
We compare the complexities of two fundamental distributed coordination problems, distributed counting and distributed queuing, in a concurrent setting. In both distributed counting and queuing, processors in a distributed system ...
展开
We compare the complexities of two fundamental distributed coordination problems, distributed counting and distributed queuing, in a concurrent setting. In both distributed counting and queuing, processors in a distributed system issue operations which are organized into a total order. In counting, each participating processor receives the rank of its operation in the total order, where as in queuing, a processor receives the identity of its predecessor in the total order. Many coordination applications can be solved using either distributed counting or queuing, and it is useful to know which of counting or queuing is the easier problem. Our results show that concurrent counting is harder than concurrent queuing on a variety of processor interconnection topologies, including high and low diameter graphs. For all these topologies, we show that the concurrent delay complexity of a particular solution to queuing, the arrow protocol, is asymptotically smaller than a lower bound on the complexity of any solution to counting.
收起
原文获取