Estimating the Concentration of Propagules of a Plant Pathogen from Soil Dilution Plate Counts when the Response is Non-linear

The estimation of micro-organism concentrations from dilution plate data is discussed for situations where expected counts are not proportional to the amount of sample per plate. Aspects of design and analysis are investigated in relation to an alternative non-linear model in which the concentration is given by the slope at the origin. This exponential model generally provides a good fit to available experimental data. Simulations show that estimators based on the model perform well when the response is non-linear and remain reasonably efficient when the response is linear.     

Algorithms Section: Introduction

Electronic Access to Algorithms
Applied Statistics algorithms are available on Statlib at Carnegie Mellon University and on the UK mirror of Statlib at the University of Kent. They may be accessed either via anonymous file transfer protocol (FTP) or by WWW mosaic.     

Algorithms for the construction of optimizing distributions

We will consider the following problem.Maximise Φ(p)over P={p=(p₁,P₂,…,p_j):P_j≧0,∑p_j=1}". We require to calcute an optimizing distribution. Examples arise in optimal regression design,maximum likelihood estimation and stratified sazmpling problems. A class of multiplicative algorithms, indexed by functions which depend on the derivatives of Φ(·)is considered for solving this problem.Iterations are of the form:p_j ^(r+1)αp_j ^(r)f(x_j ^(r)), where x_{j (r)}=d_j ^(r) or F_j ^(r)and d_j ^(r)=?Φ/?p_j While F_j ^(r)=D_j ^(r)?∑p_i ^(r)d_i ^(r) (a directional derivative)at p=p^(r)f(·)satisfies some suitable properties and may depend on one or more free parameters. These iterations neatly submit to the constraints ofv the problem. Some results will be reported and extensions to problems dependin on two or more distributions and to problems with additional constraints will be considered.     

Estimation procedures and prediction intervals

The starship, as an alternative or companion procedure to the bootstrap, introduced by Owen (1988), and the well known maximum likelihood estimation procedure were used to find prediction intervals for the future sample mean of an exponential distribution. Some remarks based on a simulation study are made on the differences between the two procedures.     

Power binomial exponential distribution: Modeling,simulation and application

ABSTRACT

The binomial exponential 2 (BE2) distribution was proposed by Bakouch et al. as a distribution of a random sum of independent exponential random variables, when the sample size has a zero truncated binomial distribution. In this article, we introduce a generalization of BE2 distribution which offers a more flexible model for lifetime data than the BE2 distribution. The hazard rate function of the proposed distribution can be decreasing, increasing, decreasing–increasing–decreasing and unimodal, so it turns out to be quite flexible for analyzing non-negative real life data. Some statistical properties and parameters estimation of the distribution are investigated. Three different algorithms are proposed for generating random data from the new distribution. Two real data applications regarding the strength data and Proschan's air-conditioner data are used to show that the new distribution is better than the BE2 distribution and some other well-known distributions in modeling lifetime data.     

The exponential Poisson logarithmic distribution

Abstract

In this article, we proposed a new three parameter lifetime distribution motivated mainly by lifetime issues, which generalizes the Exponential Poisson distribution proposed by Cancho et al. (2011) Cancho, V.G., Louzada-Neto, F., Barriga, G.D. (2011). The poisson-exponential lifetime distribution. Computat. Statist. Data Anal. 55:677–686.[Crossref], [Web of Science ®] , [Google Scholar]. We derive various standard mathematical properties of the proposed model including a formal proof of its probability density function and hazard rate function. The inference via the maximum likelihood approach is discussed. The performance of the maximum likelihood estimators, the likelihood ratio test and its power are studied by simulation. Finally, the proposed model is fitted to two real data sets and it is compared with several models.     

The power series skew normal class of distributions

A class of power series skew normal distributions is introduced by generalizing the geometric skew normal distribution of Kundu. Various mathematical properties are derived and estimation addressed by the method of maximum likelihood. The data application of Kundu [Sankhyā B, 76, 2014, 167–189] is revisited and the proposed class is shown to provide a better fit.     

Influence of human immunodeficiency virus infection on neurological impairment: an analysis of longitudinal binary data with informative drop-out

A study to investigate the human immunodeficiency virus (HIV) status on the course of neurological impairment, conducted by the HIV Center at Columbia University, followed a cohort of HIV positive and negative gay men for 5 years and assessed the presence or absence of neurological impairment every 6 months. Almost half of the subjects dropped out before the end of the study for reasons that might have been related to the missing neurological data. We propose likelihood-based methods for analysing such binary longitudinal data under informative and non-informative drop-out. A transition model is assumed for the binary response, and several models for the drop-out processes are considered which are functions of the response variable (neurological impairment). The likelihood ratio test is used to compare models with informative and non-informative drop-out mechanisms. Using simulations, we investigate the percentage bias and mean-squared error (MSE) of the parameter estimates in the transition model under various assumptions for the drop-out. We find evidence for informative drop-out in the study, and we illustrate that the bias and MSE for the parameters of the transition model are not directly related to the observed drop-out or missing data rates. The effect of HIV status on the neurological impairment is found to be statistically significant under each of the models considered for the drop-out, although the regression coefficient may be biased in certain cases. The presence and relative magnitude of the bias depend on factors such as the probability of drop-out conditional on the presence of neurological impairment and the prevalence of neurological impairment in the population under study.     

Identifying Guttman Structures in Incomplete Rasch Datasets

In applications of IRT, it often happens that many examinees omit a substantial proportion of item responses. This can occur for various reasons, though it may well be due to no more than the simple fact of design incompleteness. In such circumstances, literature not infrequently refers to various types of estimation problem, often in terms of generic “convergence problems” in the software used to estimate model parameters. With reference to the Partial Credit Model and the instance of data missing at random, this article demonstrates that as their number increases, so does that of anomalous datasets, intended as those not corresponding to a finite estimate of (the vector parameter that identifies) the model. Moreover, the necessary and sufficient conditions for the existence and uniqueness of the maximum likelihood estimation of the Partial Credit Model (and hence, in particular, the Rasch model) in the case of incomplete data are given – with reference to the model in its more general form, the number of response categories varying according to item. A taxonomy of possible cases of anomaly is then presented, together with an algorithm useful in diagnostics.     

Shrinkage estimation of P(Y < X) in the exponential distribution mixing with exponential distribution

ABSTRACT

The problem of estimation of R = P(Y < X) have been used in the paper. Let X has exponential distribution mixing with exponential distribution with parameters β and θ and Y independently of X has exponential distribution with parameter λ. By using a prior guess or estimate R₀, different shrinkage estimators of R are derived. Then the performance of the estimators are discussed. Finally, we compare these results with Baklizei and Dayyeh (2003) approaches.     

中国信贷市场的配适性分析

为了研究中国信贷市场供求配适性状况,以及造成中国信贷投放总量错配的主要因素,文章利用1997-2009年2季度中国信贷市场季度数据,采用最大似然方法估计信贷供求非均衡模型参数,实证结果表明：（1）信贷供给小于信贷需求为32个季度,信贷供给大于信贷需求为15个季度,其中1997-2001年以及2005-2007年存在严重的供小于求现象;而2002-2004年及2008年3季度以来存在信贷供大于求现象,其中2009年第1季度信贷超额供给占观察到的实际信贷量的比例为18.37%;（2）中国信贷市场上银行信贷能力是影响信贷供给的重要变量,信贷能力越高,社会上的贷款就越多,而2009年来的信贷大幅投放已经超过了银行的实际信贷能力。     

Maximum likelihood estimation in the proportional hazards model of random censorship

The maximum likelihood estimator (MLE) for the survival function S_Tunder the proportional hazards model of censorship is derived and shown to differ from the Abdushukurov-Cheng-Lin estimator when the class of allowable distributions includes all continuous and discrete distributions. The estimators are compared via an example. The MLE is calculated using a Newton-Raphson iterative procedure and implemented via a FORTRAN algorithm.     

Bootstrapping a time series model: some empirical results

The bootstrap is a methodology for estimating standard errors. The idea is to use a Monte Carlo simulation experiment based on a nonparametric estimate of the error distribution. The main objective of this article is to demonstrate the use of the bootstrap to attach standard errors to coefficient estimates in a second-order autoregressive model fitted by least squares and maximum likelihood estimation. Additionally, a comparison of the bootstrap and the conventional methodology is made. As it turns out, the conventional asymptotic formulae (both the least squares and maximum likelihood estimates) for estimating standard errors appear to overestimate the true standard errors. But there are two problems:i. The first two observations y₁ and y₂ have been fixed, and ii. The residuals have not been inflated. After these two factors are considered in the trial and bootstrap experiment, both the conventional maximum likelihood and bootstrap estimates of the standard errors appear to be performing quite well.     

Estimation of the Reliability of a Stress-Strength System from Power Lindley Distributions

In this paper, we are interested in the estimation of the reliability parameter R = P(X > Y) where X, a component strength, and Y, a component stress, are independent power Lindley random variables. The point and interval estimation of R, based on maximum likelihood, nonparametric and parametric bootstrap methods, are developed. The performance of the point estimate and confidence interval of R under the considered estimation methods is studied through extensive simulation. A numerical example, based on a real data, is presented to illustrate the proposed procedure.     

Analysis of survival data by a Weibull–Bessel distribution

In survival analysis and reliability studies, problems with random sample size arise quite frequently. More specifically, in cancer studies, the number of clonogens is unknown and the time to relapse of the cancer is defined by the minimum of the incubation times of the various clonogenic cells. In this article, we have proposed a new model where the distribution of the incubation time is taken as Weibull and the distribution of the random sample size as Bessel, giving rise to a Weibull–Bessel distribution. The maximum likelihood estimation of the model parameters is studied and a score test is developed to compare it with its special submodel, namely, exponential–Bessel distribution. To illustrate the model, two real datasets are examined, and it is shown that the proposed model, presented here, fits better than several other existing models in the literature. Extensive simulation studies are also carried out to examine the performance of the estimates.     

Covariance Matrix Formula for Exponential Family Nonlinear Models

This article gives a matrix formula for second-order covariances of maximum likelihood estimators in exponential family nonlinear models, thus generalizing the result of Cordeiro (2004 Cordeiro , G. M. ( 2004 ). Second-order covariance matrix of maximum likelihood estimates in generalized linear models . Statist. Probab. Lett. 66 : 153 – 160 .[Crossref], [Web of Science ®] , [Google Scholar]) valid for generalized linear models with known dispersion parameter. Some simulations show that the second-order covariances for exponential family nonlinear models can be quite pronounced in small to moderate sample sizes.     

A meta-analysis approach for step-stress experiments

The step-stress model is a special case of accelerated life testing that allows for testing of units under different levels of stress with changes occurring at various intermediate stages of the experiment. Interest then lies on inference for the mean lifetime at each stress level. All step-stress models discussed so far in the literature are based on a single experiment. For the situation when data have been collected from different experiments wherein all the test units had been exposed to the same levels of stress but with possibly different points of change of stress, we introduce a model that combines the different experiments and facilitates a meta-analysis for the estimation of the mean lifetimes. We then discuss in detail the likelihood inference for the case of simple step-stress experiments under exponentially distributed lifetimes with Type-II censoring.