Assessing the lifetime performance index with Lomax distribution based on progressive type I interval censored sample

In manufacturing industry, the lifetime performance index CL is applied to evaluate the larger-the-better quality features of products. It can quickly show whether the lifetime performance of products meets the desired level. In this article, first we obtain the maximum likelihood estimator of CL with two unknown parameters in the Lomax distribution on the basis of progressive type I interval censored sample. With the MLE we proposed, some asymptotic confidence intervals of CL are discussed by using the delta method. Furthermore, the MLE of CL is used to establish the hypothesis test procedure under a given lower specification limit L. In addition, we also conduct a hypothesis test procedure when the scale parameter in the Lomax distribution is given. Finally, we illustrate the proposed inspection procedures through a real example. The testing procedure algorithms presented in this paper are efficient and easy to implement.     

Parameter estimation of Cambanis-type bivariate uniform distribution with Ranked Set Sampling

The concept of ranked set sampling (RSS) is applicable whenever ranking on a set of sampling units can be done easily using a judgment method or based on an auxiliary variable. In this paper, we consider a study variable Y correlated with the auxiliary variable X and use it to rank the sampling units. Further (X,Y) is assumed to have Cambanis-type bivariate uniform (CTBU) distribution. We obtain an unbiased estimator of a scale parameter associated with the study variable Y based on different RSS schemes. We perform the efficiency comparison of the proposed estimators numerically. We present the trends in the efficiency performance of estimators under various RSS schemes with respect to parameters through line and surface plots. Further, we develop a Matlab function to simulate data from CTBU distribution and present the performance of proposed estimators through a simulation study. The results developed are implemented to real-life data also.KEYWORDS: Ranked set sampling, concomitants of order statistics, Cambanis-type bivariate uniform distribution, best linear unbiased estimatorSUBJECT CLASSIFICATIONS: 62D05, 62F07, 62G30     

Markov (Set) chains application to predict mortality rates using extended Milevsky–Promislov generalized mortality models

The mortality rates ( μx,t) measure the frequency of deaths in a fixed: population and time interval. The ability to model and forecast μx,t allows determining, among others, fundamental characteristics of life expectancy tables, e.g. used to determine the amount of premium in life insurance, adequate to the risk of death. The article proposes a new method of modelling and forecasting μx,t, using the class of stochastic Milevsky–Promislov switch models with excitations. The excitations are modelled by second, fourth and sixth order polynomials of outputs from the non-Gaussian Linear Scalar Filter (nGLSF) model and taking into account the Markov (Set) chain. The Markov (Set) chain state space is defined based on even orders of the nGLSF polynomial. The model order determines the theoretical values of the death rates. The obtained results usually provide a more precise forecast of the mortality rates than the commonly used Lee–Carter model.     

A semi-analytical solution to the maximum-likelihood fit of Poisson data to a linear model using the Cash statistic

The Cash statistic, also known as the C statistic, is commonly used for the analysis of low-count Poisson data, including data with null counts for certain values of the independent variable. The use of this statistic is especially attractive for low-count data that cannot be combined, or re-binned, without loss of resolution. This paper presents a new maximum-likelihood solution for the best-fit parameters of a linear model using the Poisson-based Cash statistic. The solution presented in this paper provides a new and simple method to measure the best-fit parameters of a linear model for any Poisson-based data, including data with null counts. In particular, the method enforces the requirement that the best-fit linear model be non-negative throughout the support of the independent variable. The method is summarized in a simple algorithm to fit Poisson counting data of any size and counting rate with a linear model, by-passing entirely the use of the traditional χ2 statistic.     

An application of a non-homogeneous Poisson model to study PM2.5 exceedances in Mexico City and Bogota

It is very important to study the occurrence of high levels of particulate matter due to the potential harm to people''s health and to the environment. In the present work we use a non-homogeneous Poisson model to analyse the rate of exceedances of particulate matter with diameter smaller that 2.5 microns (PM 2.5). Models with and without change-points are considered and they are applied to data from Bogota, Colombia, and Mexico City, Mexico. Results show that whereas in Bogota larger particles pose a more serious problem, in Mexico City, even though nowadays levels are more controlled, in the recent past PM 2.5 were the ones causing serious problems.     

The CUSUM statistics of change-point models based on dependent sequences

In this paper, we investigate the mean change-point models based on associated sequences. Under some weak conditions, we obtain a limit distribution of CUSUM statistic which can be used to judge the mean change-mount δn is satisfied or dissatisfied n1/2δn=o(1). We also study the consistency of sample covariances and change-point location statistics. Based on Normality and Lognormality data, some simulations such as empirical sizes, empirical powers and convergence are presented to test our results. As an important application, we use CUSUM statistics to do the mean change-point analysis for a financial series.     

Birnbaum–Saunders sample selection model

The sample selection bias problem occurs when the outcome of interest is only observed according to some selection rule, where there is a dependence structure between the outcome and the selection rule. In a pioneering work, J. Heckman proposed a sample selection model based on a bivariate normal distribution for dealing with this problem. Due to the non-robustness of the normal distribution, many alternatives have been introduced in the literature by assuming extensions of the normal distribution like the Student-t and skew-normal models. One common limitation of the existent sample selection models is that they require a transformation of the outcome of interest, which is common R+-valued, such as income and wage. With this, data are analyzed on a non-original scale which complicates the interpretation of the parameters. In this paper, we propose a sample selection model based on the bivariate Birnbaum–Saunders distribution, which has the same number of parameters that the classical Heckman model. Further, our associated outcome equation is R+-valued. We discuss estimation by maximum likelihood and present some Monte Carlo simulation studies. An empirical application to the ambulatory expenditures data from the 2001 Medical Expenditure Panel Survey is presented.     

Elastic statistical analysis of interval-valued time series

We investigate the problem of statistical analysis of interval-valued time series data – two nonintersecting real-valued functions, representing lower and upper limits, over a period of time. Specifically, we pay attention to the two concepts of phase (or horizontal) variability and amplitude (or vertical) variability, and propose a phase-amplitude separation method. We view interval-valued time series as elements of a function (Hilbert) space and impose a Riemannian structure on it. We separate phase and amplitude variability in observed interval functions using a metric-based alignment solution. The key idea is to map an interval to a point in R2, view interval-valued time series as parameterized curves in R2, and borrow ideas from elastic shape analysis of planar curves, including PCA, to perform registration, summarization, analysis, and modeling of multiple series. The proposed phase-amplitude separation provides a new way of PCA and modeling for interval-valued time series, and enables shape clustering of interval-valued time series. We apply this framework to three different applications, including finance, meteorology and physiology, proves the effectiveness of proposed methods, and discovers some underlying patterns in the data. Experimental results on simulated data show that our method applies to the point-valued time series.     

Investigation of the correlation of successive earthquakes preceding main shocks in the Greek territory

The Canonical Correlation Analysis (CCA) estimates the correlation between two vector variables by maximizing the correlation of linear combinations of their respective components. Here, the CCA is used to find correlation patterns in the last five successive, per pairs, earthquakes ( M≥4.0) preceding 271 main shocks ( M≥5.5) that occurred in the Greek territory during 1964–2018. The vector variables have two components, the earthquake magnitude and interevent time. The statistical significance of CCA is determined by the standard parametric test along with two proposed randomization tests, one using random shuffling of each paired dataset and one using randomly selected pairs of successive earthquakes. Simulations were designed on synthetic data from vector variables having the statistical characteristics of the real observations. The results on uncorrelated variables showed the correct size for the two randomization tests but larger type I error for the parametric significance test for small sample size. For correlated variables, the test power was equally high for both test types. The application of CCA and the significance tests to the Greek seismicity evidence the significant correlation among the last five successive preshocks, proving to be a promising tool in an a posteriori short-term earthquake forecasting.KEYWORDS: Canonical correlation analysis (CCA), randomization significance test, preshock & main shock, Greek seismicity, a posteriori short-term earthquake forecasting     

Bayesian rank-based hypothesis testing for the rank sum test,the signed rank test,and Spearman's ρ

Bayesian inference for rank-order problems is frustrated by the absence of an explicit likelihood function. This hurdle can be overcome by assuming a latent normal representation that is consistent with the ordinal information in the data: the observed ranks are conceptualized as an impoverished reflection of an underlying continuous scale, and inference concerns the parameters that govern the latent representation. We apply this generic data-augmentation method to obtain Bayes factors for three popular rank-based tests: the rank sum test, the signed rank test, and Spearman''s ρs.     

Statistical Analysis Of Cometary Data

In this study an attempt is made to assess statistically the validity of two theories as to the origin of comets. This subject still leads to great controversy amongst astronomers but recently two main schools of thought have developed.

These are that comets are of

(i) planetary origin,

(ii) interstellar origin.

Many theories have been expanded within each school of thought but at the present time one theory in each is generally accepted. This paper sets out to identify the statistical implications of each theory and evaluate each theory in terms of their implications.