Objective Bayesian Analysis of an Exponential Regression Model with Constrained Parameters Applied to Animal Digestibility

In animal digestibility the proportion of degraded food along the time has usually been modeled as a normal random variable with mean a function of the time and the following three parameters: the proportion of degraded food almost instantaneously, remaining proportion of food to be degraded, and velocity of degradation. The estimation of these parameters has been carried out mainly from a frequentist viewpoint by using the asymptotic distribution of the maximum likelihood estimator. This may give inadmissible estimates, such as values outside of the range of the parameters. This drawback could not appear if a Bayesian approach were adopted. In this article an objective Bayesian analysis is developed and illustrated on real and simulated data.     

An Inverse-Probability-Weighted Approach to the Estimation of Successive Duration Times under Left-Truncation and Right-Censoring

In incident cohort studies, survival data often include subjects who have had an initiate event at recruitment and may potentially experience two successive events (first and second) during the follow-up period. Since the second duration process becomes observable only if the first event has occurred, left-truncation and dependent censoring arise if the two duration times are correlated. To confront the two potential sampling biases, Chang and Tzeng (2006 Chang , S.-H. , Tzeng , S.-J. (2006). Noparametric estimation of sojourn time distributions for truncated serial event data- a weight-adjusted approach. Lifetime Data Anal. 53–67.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) provided an inverse-probability-weighted (IPW) approach for estimating the joint probability function of successive duration times. In this note, an alternative IPW approach is proposed. A simulation study is conducted to compare the two IPW approaches.     

Mixed Graphical Model Selection Using Holm's Procedure

The problem of selecting a graphical model is considered as a performing simultaneously multiple tests. The control of the overall Type I error on the selected graph is done using the so famous Holm's procedure. We prove that when we use a consistent edge exclusion test the selected graph is asymptotically equal to the true graph with probability at least equal to a fixed level 1 ? α. This method is then used for the selection of mixed concentration graph models by performing the χ²-edge exclusion test. We also apply the method to two classical examples and to simulated data. We compare the overall error of the selected model with the one obtained using the stepwise method. We establish that the control is better when we use the Holm's procedure.     

On Unimodal Regression in the Exponential Family

In this article, we discuss statistical methods for curve-estimation under the assumption of unimodality for variables with distributions belonging to the two-parameter exponential family with known or constant dispersion parameter. An important special case is a one-parameter distribution. We suggest a nonparametric method based on monotonicity properties. The method is applied to Swedish data on laboratory verified diagnoses of influenza and data on inflation from an episode of hyperinflation in Bulgaria.     

Generalized Linear Failure Rate Distribution

The exponential and Rayleigh are the two most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. Unfortunately, the exponential distribution only has constant failure rate and the Rayleigh distribution has increasing failure rate. The linear failure rate distribution generalizes both these distributions which may have non increasing hazard function also. This article introduces a new distribution, which generalizes linear failure rate distribution. This distribution generalizes the well-known (1) exponential distribution, (2) linear failure rate distribution, (3) generalized exponential distribution, and (4) generalized Rayleigh distribution. The properties of this distribution are discussed in this article. The maximum likelihood estimates of the unknown parameters are obtained. A real data set is analyzed and it is observed that the present distribution can provide a better fit than some other very well-known distributions.     

Classification of Observations into One of Two Artificially Dichotomized Classes by Using a Normal Screening Variable

This article considers a problem of normal based two group classification when the groups are artificially dichotomized by a screening variable. Each group distribution is derived and the best regions for the classification are obtained. These derivations yield yet another classification rule. The rule is studied from several aspects such as the distribution of the rule, the optimal error rate, and the testing of a hypothesis. This article gives relationships among these aspects along with the investigation of the performance of the rule. The classification method and ideas are illustrated in detail with two examples.     

An Autoregressive Model for Time Series of Circular Data

This article focuses on estimating an autoregressive regression model for circular time series data. Simulation studies have shown the difficulties involved in obtaining good estimates from low concentration data or from small samples. It presents an application using real data.     

The Beta Product Distribution with Complex Parameters

The family consisting of the distributions of products of two independent beta variables is extended to include cases where some of the parameters are not positive but negative or complex. This “beta product” distribution is expressible as a Meijer G function. An example (from risk theory) where such a distribution arises is given: an infinite sum of products of independent random variables is shown to have a distribution that is the product convolution of a complex-parameter beta product and an independent exponential. The distribution of the infinite sum is a new explicit solution of the stochastic equation X = (in law) B(X + C). Characterizations of some G distributions are also proved.     

Inference for a Simple Step-Stress Model with Type-I Censoring and Lognormally Distributed Lifetimes

Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows the experimenter to obtain failure data more quickly at increased stress levels than under normal operating conditions. A step-stress model is one special class of ALT, and in this article we consider a simple step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-I censoring. We then discuss inferential methods for the unknown parameters of the model by the maximum likelihood estimation method. Some numerical methods, such as the Newton–Raphson and quasi-Newton methods, are discussed for solving the corresponding non-linear likelihood equations. Next, we discuss the construction of confidence intervals for the unknown parameters based on (i) the asymptotic normality of the maximum likelihood estimators (MLEs), and (ii) parametric bootstrap resampling technique. A Monte Carlo simulation study is carried out to examine the performance of these methods of inference. Finally, a numerical example is presented in order to illustrate all the methods of inference developed here.     

Dependent Insurance Risk Model: Deterministic Threshold

This article considers a dependent insurance risk model. We assume that the inter-arrival time depends on the previous claim size through a deterministic threshold structure. Adjustment coefficient and Lundberg-type upper bound for the ruin probability are obtained. In case of exponential claim size, an explicit solution for the ruin probability is obtained by solving a system of ordinary delay differential equations. Some numerical results are included for illustration purposes.