Parameter measures of skewness

Several different measures of skewness are commonly used in place of γ₁, the third central moment divided by the cube of the standard deviation. The numerical values of these measures are compared in this paper for members of the gamma, lognormal or Weibull family of distributions and shown to vary considerably in most cases even when skewness and kurtosis are moderate.     

Estimating the probability of obtaining nonfeasible parameter estimates of the generalized pareto distribution

In this paper we consider the problem of estimating the parameters of the generalized Pareto distribution. Both the method of moments and probability-weighted moments do not guarantee that their respective estimates will be consistent with the observed data. We present simple programs to predict the probability of obtaining such nonfeasible estimates. Our estimation techniques are based on results from intensive simulations and the successful modelling of the lower tail of the distribution of the upper bound of the support. More simulations are performed to validate the new procedure.     

海杂波背景下的双参数单元平均恒虚警检测器

介绍了海杂波的幅度分布模型,指出了对于同一门限系数"尖锐"海杂波背景下的虚警率要明显高于噪声背景下的虚警率,提出了双参数单元平均恒虚警(CA-CFAR)检测器的结构框图,仿真分析了其检测性能.最后分别利用双参数CA-CFAR检测器和常规CA-CFAR检测方法对实测数据进行处理和比较,指出在虚警率一定的前提下前者相对于后两者在空间上可以自适应地改变门限系数以有效地抑制海杂波引起的高虚警.     

The cross-product ratio in bivariate lognormal and gamma distributions,with an application to non-randomized trials

Non-randomized trials can give a biased impression of the effectiveness of any intervention. We consider trials in which incidence rates are compared in two areas over two periods. Typically, one area receives an intervention, whereas the other does not. We outline and illustrate a method to estimate the bias in such trials under two different bivariate models. The illustrations use data in which no particular intervention is operating. The purpose is to illustrate the size of the bias that could be observed purely due to regression towards the mean (RTM). The illustrations show that the bias can be appreciably different from zero, and even when centred on zero, the variance of the bias can be large. We conclude that the results of non-randomized trials should be treated with caution, as interventions which show small effects could be explained as artefacts of RTM.     

A non‐linear model of fecundability,postpartum amenorrhea,and sterility*

This paper proposes a convolution model of fecundability, controling for the effects of postpartum amenorrhea and unobserved heterogeneity in fecundability. Simulation analysis was used to assess the validity and reliability of estimates derived from the model. Analysis showed that the model captured the mean and standard deviation of age at the onset of sterility in simulated populations where sterility followed either a Gompertz, a gamma, or a lognormal distribution. The model performed well when sterility was specified by either a lognormal or a gamma distribution. The model also accurately estimated fecundability and postpartum amenorrhea. Next, the model was found to fit data from 17th and 18th century French Canadian birth histories. In this French Canadian sample the mean age at sterility was found to be 46.3 years using a gamma model. The decline in fecundability was almost linear after age 30. Thus, fecundability at age 40 had declined to about one‐third of that observed at age 30. Variability in individual fecundability was quite high. For example, women with fecundability one standard deviation above the mean had about 2.3 times as high fecundability as women one standard deviation below the mean.     

Confidence intervals for lognormal regression and a non-parametric alternative

Approximate confidence intervals are given for the lognormal regression problem. The error in the nominal level can be reduced to O(n ^?2), where n is the sample size. An alternative procedure is given which avoids the non-robust assumption of lognormality. This amounts to finding a confidence interval based on M-estimates for a general smooth function of both ? and F, where ? are the parameters of the general (possibly nonlinear) regression problem and F is the unknown distribution function of the residuals. The derived intervals are compared using theory, simulation and real data sets.     

A general algorithm for computing simultaneous prediction intervals for the (log)-location-scale family of distributions

Making predictions of future realized values of random variables based on currently available data is a frequent task in statistical applications. In some applications, the interest is to obtain a two-sided simultaneous prediction interval (SPI) to contain at least k out of m future observations with a certain confidence level based on n previous observations from the same distribution. A closely related problem is to obtain a one-sided upper (or lower) simultaneous prediction bound (SPB) to exceed (or be exceeded) by at least k out of m future observations. In this paper, we provide a general approach for computing SPIs and SPBs based on data from a particular member of the (log)-location-scale family of distributions with complete or right censored data. The proposed simulation-based procedure can provide exact coverage probability for complete and Type II censored data. For Type I censored data, our simulation results show that our procedure provides satisfactory results in small samples. We use three applications to illustrate the proposed simultaneous prediction intervals and bounds.     

Lognormal Distributions for Fish Consumption by the General U.S. Population

The rate of fish consumption is a critical variable in the assessment of human health risk from water bodies affected by chemical contamination and in the establishment of federal and state Ambient Water Quality Criteria (AWQC). For 1973 and 1974, the National Marine Fisheries Service (NMFS) analyzed data on the consumption of salt-water finfish, shellfish, and freshwater finfish from all sources in 10 regions of the United States for three age groups in the general population: children (ages 1 through 11 years), teenagers (ages 12 through 18 years), and adults (ages 19 through 98 years). Even though the NMFS data reported in Ref. 14 are 20 years old, they remain the most complete data on the overall consumption of all fish by the general U.S. population and they have been widely used to select point values for consumption. Using three methods, we fit lognormal distributions to the results of the survey as analyzed and published in Ref. 14. Strong lognormal fits were obtained for most of the 90 separate data sets. These results cannot necessarily be used to model the consumption of fish by sport or subsistence anglers from specific sites or from single water bodies.     

The Anderson–Darling Goodness-of-Fit Test Statistic for the Three-Parameter Lognormal Distribution

Anderson–Darling goodness-of-fit test percentage points are given for the three-parameter lognormal distribution for both the cases of positive skewness and a lower bound and negative skewness and an upper bound. The focus is on the most practical case when all parameters are unknown and must be estimated from the sample data. Fitted response functions for the critical values based on the shape parameter and sample size are reported to avoid using a vast array of tables.     

Performance of confidence interval tests for the ratio of two lognormal means applied to Weibull and gamma distribution data

Five estimation approaches have been developed to compute the confidence interval (CI) for the ratio of two lognormal means: (1) T, the CI based on the t-test procedure; (2) ML, a traditional maximum likelihood-based approach; (3) BT, a bootstrap approach; (4) R, the signed log-likelihood ratio statistic; and (5) R*, the modified signed log-likelihood ratio statistic. The purpose of this study was to assess the performance of these five approaches when applied to distributions other than lognormal distribution, for which they were derived. Performance was assessed in terms of average length and coverage probability of the CIs for each estimation approaches (i.e., T, ML, BT, R, and R*) when data followed a Weibull or gamma distribution. Four models were discussed in this study. In Model 1, the sample sizes and variances were equal within the two groups. In Model 2, the sample sizes were equal but variances were different within the two groups. In Model 3, the variances were different within the two groups and the larger variance was paired with the larger sample size. In Model 4, the variances were different within the two groups and the larger variance was paired with the smaller sample size. The results showed that when the variances of the two groups were equal, the t-test performed well, no matter what the underlying distribution was and how large the variances of the two groups were. The BT approach performed better than the others when the underlying distribution was not lognormal distribution, although it was inaccurate when the variances were large. The R* test did not perform well when the underlying distribution was Weibull or gamma distributed data, but it performed best when the data followed a lognormal distribution.