On the Estimation of Parameters of Kumaraswamy-G Distributions

Cordeiro and de Castro proposed a new family of generalized distributions based on the Kumaraswamy distribution (denoted as Kw-G). Nadarajah et al. showed that the density function of the new family of distributions can be expressed as a linear combination of the density of exponentiated family of distributions. They derived some properties of Kw-G distributions and discussed estimation of parameters using the maximum likelihood (ML) method. Cheng and Amin and Ranneby introduced a new method of estimating parameters based on Kullback–Leibler divergence (the maximum spacing (MSP) method). In this article, the estimates of parameters of Kw-G distributions are obtained using the MSP method. For some special Kw-G distributions, the new estimators are compared with ML estimators. It is shown by simulations and a real data application that MSP estimators have better properties than ML estimators.     

丹东重点开发开放试验区发展策略研究

以南水北调中线一期工程下穿京九铁路隧洞工程为背景,以铁路轨道静态容许偏差管理值和容许高低倾斜值为基础,结合工程特点,通过对比经验公式及数值计算结果,提出了三孔小净距隧洞下穿铁路干线地表沉降控制标准,并采用总控制指标与分阶段控制指标相结合的方式建立监控量测管理标准。实际工程通过采用系列控制措施,施工全过程可控,实测地表沉降小于控制标准值,保证了铁路正常运营安全、隧洞施工安全和施工质量。     

Asymptotic normality of generalized maximum spacing estimators for multivariate observations

In this paper, the maximum spacing method is considered for multivariate observations. Nearest neighbor balls are used as a multidimensional analogue to univariate spacings. A class of information-type measures is used to generalize the concept of maximum spacing estimators of model parameters. Asymptotic normality of these generalized maximum spacing estimators is proved when the assigned model class is correct, that is, the true density is a member of the model class.     

Addendum to fitting polynomials to main effects in multi factor experiments: A note concerning polynomial coefficients when all factors are quantitative

When all factors are quantitative, cell means may be expressed as a polynomial function of products of powers of the associated quantitative classification variables. Existence and uniqueness of this polynomial is established for unbalanced data with unequal spacing for no missing cells. The relationship between the coefficients of this polynomial and the main effects polynomials are derived for main effects which are arbitrary weighted averages of the cell means.     

低渗透油藏考虑压裂的合理注采井距研究

基于点源点汇渗流理论，推导了低渗透油藏考虑压裂措施的注采井间压力梯度分布方程，结合启动压力梯度 与低渗透油藏渗透率关系式提出了合理注采井距计算方法，并结合低渗透油藏实例，进行了注采井间压力梯度影响因 素分析，得到了低渗透油藏合理注采井距理论图版，验证了该方法的可靠性。结果表明：在渗透率、注采压差和压裂裂 缝长度一定的情况下，存在合理的注采井距，且合理井距随渗透率、注采压差和裂缝半长的增加而增大；认为采取压裂 等增产措施，有利于建立起有效的驱替压力系统，能较大幅度地提高合理注采井距。推导出的考虑压裂的注采井间压 力梯度表达式能够较准确地反映真实地层驱替压力系统，研究结果对合理开发低渗透油藏具有一定的实际意义。     

On goodness of fit tests based on spacings for type ii censored samples

A class of tests based on spacings is obtained for milticensored samples. Their asymptotic null as well as alternative distributions are obtained.     

Powerful Parametric Tests Based on Sum‐Functions of Spacings

Assume that we have a sequence of n independent and identically distributed random variables with a continuous distribution function F, which is specified up to a few unknown parameters. In this paper, tests based on sum‐functions of sample spacings are proposed, and large sample theory of the tests are presented under simple null hypotheses as well as under close alternatives. Tests, which are optimal within this class, are constructed, and it is noted that these tests have properties that closely parallel those of the likelihood ratio test in regular parametric models. Some examples are given, which show that the proposed tests work also in situations where the likelihood ratio test breaks down. Extensions to more general hypotheses are discussed.     

The Logistic-Uniform Distribution and Its Applications

In this article, we give a new family of univariate distributions generated by the Logistic random variable. A special case of this family is the Logistic-Uniform distribution. We show that the Logistic-Uniform distribution provides great flexibility in modeling for symmetric, negatively and positively skewed, bathtub-shaped, “J”-shaped, and reverse “J”-shaped distributions. We discuss simulation issues, estimation by the methods of moments, maximum likelihood, and the new method of minimum spacing distance estimator. We also derive Shannon entropy and asymptotic distribution of the extreme order statistics of this distribution. The new distribution can be used effectively in the analysis of survival data since the hazard function of the distribution can be “J,” bathtub, and concave-convex shaped. The usefulness of the new distribution is illustrated through two real datasets by showing that it is more flexible in analyzing the data than the Beta Generalized-Exponential, Beta-Exponential, Beta-Normal, Beta-Laplace, Beta Generalized half-Normal, β-Birnbaum-Saunders, Gamma-Uniform, Beta Generalized Pareto, Beta Modified Weibull, Beta-Pareto, Generalized Modified Weibull, Beta-Weibull, and Modified-Weibull distributions.     

Estimating the quantile function of a location-scale family of distributions based on few selected order statistics

Some general asymptotic methods of estimating the quantile function, Q(ξ), 0<ξ<1, of location-scale families of distributions based on a few selected order statistics are considered, with applications to some nonregular distributions. Specific results are discussed for the ABLUE of Q(ξ) for the location-scale exponential and double exponential distributions. As a further application of the exponential results, we discuss a nonlinear estimator of Q(ξ) for the scale-shape Pareto distribution.     

Alternatives to maximum likelihood estimation based on spacings and the Kullback–Leibler divergence

An alternative to the maximum likelihood (ML) method, the maximum spacing (MSP) method, is introduced in Cheng and Amin [1983. Estimating parameters in continuous univariate distributions with a shifted origin. J. Roy. Statist. Soc. Ser. B 45, 394–403], and independently in Ranneby [1984. The maximum spacing method. An estimation method related to the maximum likelihood method. Scand. J. Statist. 11, 93–112]. The method, as described by Ranneby [1984. The maximum spacing method. An estimation method related to the maximum likelihood method. Scand. J. Statist. 11, 93–112], is derived from an approximation of the Kullback–Leibler divergence. Since the introduction of the MSP method, several closely related methods have been suggested. This article is a survey of such methods based on spacings and the Kullback–Leibler divergence. These estimation methods possess good properties and they work in situations where the ML method does not. Important issues such as the handling of ties and incomplete data are discussed, and it is argued that by using Moran's [1951. The random division of an interval—Part II. J. Roy. Statist. Soc. Ser. B 13, 147–150] statistic, on which the MSP method is based, we can effectively combine: (a) a test on whether an assigned model of distribution functions is correct or not, (b) an asymptotically efficient estimation of an unknown parameter _θ0${\theta }_0$, and (c) a computation of a confidence region for _θ0${\theta }_0$.