A Simple Option-Pricing Formula

A simple option-pricing formula based on the Weibull distribution is introduced. The simplicity of the algebraic form and ease of implementation are comparable to those of Black-Scholes. Application to S&P 500 options shows that the pricing biases present in the Black-Scholes model are eliminated. Prices produced by the presented model generally lie within or close to the bid-ask spread. For long-term options (over one year), the Weibull formula exhibits significantly higher precision than the Black-Scholes formula does. While a rigorous comparison of all available models is necessary, the simplicity and precision of the proposed model are its main advantages over the existing models.     

Periodical Preventive-Maintenance Contract for a Leased Facility with Weibull Life-Time

This paper develops a mathematical model to derive the optimal periodical preventive maintenance (PM) policy for a leased facility with Weibull life-time. Within a lease period, any failures of the facility are rectified by minimal repairs and a penalty may occur to the lessor when the time required to perform a minimal repair exceeds a reasonable time limit. To reduce failures of the facility, additional PM actions are carried out periodically during the lease period. When the life-time distribution of a product is Weibull, the optimal number of PM actions and the corresponding maintenance degrees are derived such that the expected total maintenance cost is minimized. The structural properties of the optimal policy are investigated and an efficient algorithm is provided to search for the optimal policy. Finally, numerical examples are provided to illustrate the features of the proposed model.     

Weibull分布航天产品可靠性评估的MMLE-Bayes方法

航天产品现场使用数据具有小子样、零失效的特点，要实现其工程化可靠性评估，需要充分利用各种环境下的试验信息和相似型号产品的试验信息及使用信息，因此，提出了一种适用于Weibull分布航天产品可靠性综合评估的MMLE—Bayes方法。首先通过MMLE方法得到额定任务时间可靠度的置信下限估计，再通过构造合理的验前分布实现Bayes可靠性评估。在此过程中，为合理融合各来源的验前信息，提出了环境因子和相似因子的概念及其估计方法。最后通过一种航天产品的可靠性评估实例，说明了MMLE—Bayes—Weibull方法的的实用性和有效性。     

Tests for location-scale families based on the empirical characteristic function

A class of procedures is presented for using random samples to test the fit of location-scale families—distributions F(·;θ₁,θ₂) such that Z=(X−θ₁)/θ₂ has distribution Working with empirically standardized data, the test statistic is a measure of distance between the empirical characteristic function, and the c.f. of Z under the null hypothesis, ϕ₀(t). The closed-form test statistic is derived by integrating over the product of a weight function times Using as weight function for each location-scale family the squared modulus of ϕ₀ itself presents a unified test procedure. Included as special cases are well-known tests for normal and Cauchy laws. Small-sample powers are compared with those of Anderson-Darling tests for each of seven univariate location-scale families.     

Trivariate non‐Gaussian copulas to analyze the spatial behavior of rat sightings

The brown rat lives with man in a wide variety of environmental contexts and adversely affects public health by transmission of diseases, bites, and allergies. Understanding behavioral and spatial correlation aspects of pest species can contribute to their effective management and control. Rat sightings can be described by spatial coordinates in a particular region of interest defining a spatial point pattern. In this paper, we investigate the spatial structure of rat sightings in the Latina district of Madrid (Spain) and its relation to a number of distance‐based covariates that relate to the proliferation of rats. Given a number of locations, biologically considered as attractor points, the spatial dependence is modeled by distance‐based covariates and angular orientations through copula functions. We build a particular spatial trivariate distribution using univariate margins coming from the covariate information and provide predictive distributions for such distances and angular orientations.     

A Simple Derivation of Moments of the Exponentiated Weibull Distribution

The Exponentiated Weibull family is an extension of the Weibull family obtained by adding an additional shape parameter. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates which are quite common in reliability and biological studies. As with any other distribution, many of its interesting characteristics and features can be studied through moments. Presently, moments of this distribution are available only under certain restrictions. In this paper, a general derivation of moments without any restriction whatsoever is proposed. A compact expression for moments is presented.     

Modeling claims data with composite Stoppa models

In this paper, a new class of composite model is proposed for modeling actuarial claims data of mixed sizes. The model is developed using the Stoppa distribution and a mode-matching procedure. The use of the Stoppa distribution allows for more flexibility over the thickness of the tail, and the mode-matching procedure gives a simple derivation of the model compositing with a variety of distributions. In particular, the Weibull–Stoppa and the Lognormal–Stoppa distributions are investigated. Their performance is compared with existing composite models in the context of the well-known Danish fire insurance data-set. The results suggest the composite Weibull–Stoppa model outperforms the existing composite models in all seven goodness-of-fit measures considered.     

Duration dependence in US business cycles: An analysis using the modulated power law process

The modulated power law process is used to analyze the duration dependence in US business cycles. The model makes less restricting assumptions than traditional models do and measures both the local and global performance of business cycles. The results indicate evidence of positive duration dependence in the U.S. business cycles. Structural change after WWII in both expansion and contraction phases of business cycles is also documented. Hypothesis tests confirm that the model fits US business cycles.      

Slow convergence of the number of near-maxima for Burr XII distributions

A near-maximum is an observation which falls within a distance a of the maximum observation in an independent and identically distributed sample of size n. Subject to some conditions on the tail thickness of the population distribution, the number K _n (a) of near-maxima is known to converge in probability to one or infinity, or in distribution to a shifted geometric law. In this paper we show that for all Burr XII distributions K _n (a) converges almost surely to unity, but this convergence property may not become clear under certain cases even for very large n. We explore the reason of such slow convergence by studying a distributional continuity between Burr XII and Weibull distributions. We have also given a theoretical explanation of slow convergence of K _n (a) for the Burr XII distributions by showing that the rate of convergence in terms of P{K _n (a) > 1} tending to zero changes very little with the sample size n. Illustrations of the limiting behaviour K _n (a) for the Burr XII and the Weibull distributions are given by simulations and real data. The study also raises an important issue that although the Burr XII provides overall better fit to a given data set than the Weibull distribution, cautions should be taken for the extrapolation of the upper tail behaviour in the case of slow convergence.