Edward L. Melnick

Misspecifications of the Normal Distribution

Abstract Incorrect statements about the normal distribution are discussed and illustrated with counterexamples.

Creating Value in Financial Services

Financial services firms everywhere have undergone major changes over the last several decades. These firms include retail commercial banks, investment banks, insurance companies, mutual fund companies, securities brokers, and credit card companies. The decade of the nineties has witnessed a significant number of mergers among these firms worldwide. Some mergers were intended to achieve economies of scale from greater size and geographic diversity, e.g., the merger of Chase and Chemical. Some mergers were intended to establish a bridge between different financial services in the hope of creating synergies e.g., the merger of Travelers Group with Citicorp.

Approximate simultaneous prediction intervals for multiple forecasts

A general procedure including a simple computational algorithm is presented for the construction of approximate (conservative) simultaneous prediction intervals for L ≥ 2 forecasts generated by an autoregressive integrated moving average (ARIMA) model. For models with a monotone non-increasing autocorrelation function of forecast errors (absolute value) further simplification in computations is obtained. Details are given for two important special cases, an AR(l) model and an exponential smoothing model. These two cases are also illustrated with data on hourly measures of viscosity from a chemical process.

Filter design for the seasonal adjustment of a time series

Studying the fluctuations of a time series is made easier if the seasonal component is eliminated. This paper describes a new approach to seasonal adjustment which not only considers the effect of the seasonal variation upon the observed phenomena, but also the relationship between the desired accuracy of the adjust¬ment and its resulting properties. An algorithm is presented which develops moving average filters for seasonally adjusting the data. The output of the algorithm is discussed in terms of criteria proposed for evaluating seasonal adjustments.

Moments of ranked discrete variables with an application to independent poisson variates

This paper presents a method for computing moments of ranked discrete variates. The method is based on a recursive relationship between the moments of the rth order statistic and the moments of the extreme order statistics. Bounds on the estimated moments are constructed as a function of truncation error and computational round-off errors. The method is illustrated with independent Poisson variates where the mean and variance of the smallest and largest of n ranked Poisson variates for n = 1(1)20 and Poisson parameter λ = 1(1)10 are computed. An approximation for the mean of an ordered Poisson variate is presented.

An application of the simplex method for estimation problems related to contingency tables

The problem considered hers is the adjustment of cross-tabulated sampled data which tit known marginal totals but retain their original relationships to each other as measured by a statistical criterion (e.g., the minimisation of Neymans modified chi-squars, the maximisation of the Likelihood function, the minimisation or the discrimination information number). In this paper a mathematical model and algorithm are presented from which the adjusted cell counts are computed so that they satisfy exactly any of the proposed statistical criteria subject to the marginal constraints. These integer valued estimates are obtained in a finite number of iterations using readily available computer programs.

Estimation of Mortality Rates From Insurance Data

The problem of using insurance intercompany data to determine mortality rates has had a long history of development. The development of these mortality rates involves two steps, namely, the estimation of the rates from the data and the interpolation and smoothing of these rates to conform to known trends in the mortality rates by age, and time since first insured. This paper will discuss the different methods used to determine these rates and discuss the advantages and disadvantages of each approach. Keywords: mortality; estimation; smoothing; select mortality; ultimate mortality

Copulas and Other Measures of Dependency

Copulas have been developed for modeling the probability distribution of a multivariate random variable. The technique includes generating distributions with asymmetrical tail dependence structure, which is important in extreme value theory. Keywords: families of copulas; measures of dependency; modeling multivariate distributions

Modeling Services of Financial Institutions in Emerging Markets

The success of financial institutions expanding into emerging markets is a function of the services provided. Competitive positioning of institutions relative to competitors includes location of customer access, services provided, and timing and quality of service. The methodology described in this chapter is intended to infer strategies that will optimize management’s objectives and indicate changing dynamics in the marketplace.