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Gutiérrez, R.; Angulo, J. M.; González, A.; Pérez, R.
1991 Applied Stochastic Models and Data Analysis
The multidimensional lognormal diffusion process with exogenous factors is treated using the Kolmogorov equations, and the mean vector and covariance matrix are estimated using discrete sampling by the maximum‐likelihood method. Also, this process is constructed as a solution of a multidimensional stochastic differential equation, and an estimation is made through the maximum‐likelihood method to infer the parameters of the exogenous factors, this time using continuous sampling. Finally, a test for a hypothesis based on these parameters is constructed.
1991 Applied Stochastic Models and Data Analysis
This paper presents the problem of the evaluation of the maximum likelihood estimator, when the likelihood function has multiple maxima, using the stochastic algorithm called ‘simulated annealing’. Analysis of the particular case of the decomposition of a mixture of five univariate normal distributions shows the properties of this methodology with respect to the E—M algorithm. The results are compared considering some distance measures between the estimated distribution functions and the true one.
1991 Applied Stochastic Models and Data Analysis
One of the most important variables for manpower planners is duration until a specified event occurs. This is frequently the completed length of service until leaving a job, but may also include such variables as length of service in a grade until promotion, or length of a spell of withdrawal from the labour force.
1991 Applied Stochastic Models and Data Analysis
A hierarchical production control framework for a flexible manufacturing system is proposed. The machines in the system are subject to failures in a wide spectrum band. At first, failures are clustered near some discrete points on the failure spectrum in order to define the hierarchical model. Each level in the hierarchy corresponds to a discrete point on the failure spectrum. At each level, faster varying failures are modelled by their mean behaviour, and more slowly varying failures are treated as static. Then, a hierarchical controller of multiple time scale type is proposed. System control at each level is based on the work of Kimemia and Gershwin. Simulation results conclude the paper.
Page, Dominique; Tremolieres, Raymond
1991 Applied Stochastic Models and Data Analysis
This article presents a model of insurance and investment risk diversification. An in‐depth analysis of the mathematical formulation of the risk is presented. In this regard, we introduce a new concept called the substitution principle to formulate the model rigorously. We show that, if the investment risks are normally non‐linear, the insurance risks are linear in nature. This proves that the well‐known diversification principle has to be viewed differently in finance and in insurance.
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