Models involving two inverse Weibull distributions

In this paper, we look at three models (mixture, competing risk and multiplicative) involving two inverse Weibull distributions. We study the shapes of the density and failure-rate functions and discuss graphical methods to determine if a given data set can be modelled by one of these models. (C) 2001 Elsevier Science Ltd. All rights reserved.

n-fold Weibull multiplicative model

In this paper we study the n-fold multiplicative model involving Weibull distributions and examine some properties of the model. These include the shapes for the density and failure rate functions and the WPP plot. These allow one to decide if a given data set can be adequately modelled by the model. We also discuss the estimation of model parameters based on the WPP plot. (C) 2001 Elsevier Science Ltd. All rights reserved.

Recent trends in pay equity: Beyond the aggregate statistics

The earnings gap between men and women has remained comparatively stable at an aggregate level over the 1990s in Australia. From one perspective, this is a reminder of the considerable difficulty of addressing wage differentials once the most overt forms of wage discrimination have been removed, and of the limited impact of most policy initiatives. From another, it may be seen as evidence that dire predictions about the effects of decentralisation on the earnings gap have failed to materialise. In this paper, I use Australian Bureau of Statistics data to show that a number of different trends are evident underneath the relatively static picture shown by the aggregate statistics, particularly as wage dispersion has increased. The data suggest not only that the prospects for pay equity are far from benign, but also that in the current labour market the issue of gender pay inequality cannot be effectively addressed separately from wage inequality more generally.

Estimating and evaluating the statistics of gapped local-alignment scores

We present a novel maximum-likelihood-based algorithm for estimating the distribution of alignment scores from the scores of unrelated sequences in a database search. Using a new method for measuring the accuracy of p-values, we show that our maximum-likelihood-based algorithm is more accurate than existing regression-based and lookup table methods. We explore a more sophisticated way of modeling and estimating the score distributions (using a two-component mixture model and expectation maximization), but conclude that this does not improve significantly over simply ignoring scores with small E-values during estimation. Finally, we measure the classification accuracy of p-values estimated in different ways and observe that inaccurate p-values can, somewhat paradoxically, lead to higher classification accuracy. We explain this paradox and argue that statistical accuracy, not classification accuracy, should be the primary criterion in comparisons of similarity search methods that return p-values that adjust for target sequence length.

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Study of n-fold Weibull competing risk model

This paper deals with an n-fold Weibull competing risk model. A characterisation of the WPP plot is given along with estimation of model parameters when modelling a given data set. These are illustrated through two examples. A study of the different possible shapes for the density and failure rate functions is also presented. (C) 2003 Elsevier Ltd. All rights reserved.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Difficulties in the Learning of Statistics by the Students of the Primary Education

The present study, covering students from public schools and a private school on the island of São Miguel (Azores, Portugal), aims to meet the difficulties of the students of the 3rd and 4th years of the primary education in solving tasks involving construction, reading and interpreting tables and statistical graphs, in the context of Organization and Data Handling (ODH). We present the main results obtained from statistical methods, among which we highlight some non-parametric hypothesis tests and the Categorical Principal Component Analysis (CatPCA), given the nature of the variables included in the questionnaire (mostly nominal and ordinal variables).

Probability and statistics: selected problems

Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Statistics as a basis for discrimination in the insurance business

The European Court of Justice has held that as from 21 December 2012 insurers may no longer charge men and women differently on the basis of scientific evidence that is statistically linked to their sex, effectively prohibiting the use of sex as a factor in the calculation of premiums and benefits for the purposes of insurance and related financial services throughout the European Union. This ruling marks a sharp turn away from the traditional view that insurers should be allowed to apply just about any risk assessment criterion, so long as it is sustained by the findings of actuarial science. The naïveté behind the assumption that insurers’ recourse to statistical data and probabilistic analysis, given their scientific nature, would suffice to keep them out of harm’s way was exposed. In this article I look at the flaws of this assumption and question whether this judicial decision, whilst constituting a most welcome landmark in the pursuit of equality between men and women, has nonetheless gone too far by saying too little on the million dollar question of what separates admissible criteria of differentiation from inadmissible forms of discrimination.

Fishery statistics of the United States / prepared by Data Management and Statistics Division.

1975