STOCHASTIC MODEL FOR TIME TO RECRUITMENT IN A SINGLE GRADE MANPOWER SYSTEM WITH TWO TYPES OF INTERDECISION TIMES WHEN THE BREAKDOWN THRESHOLD HAS THREE COMPONENTS

In this paper, the problem of time to recruitment is analyzed for a single grade manpower system in which attrition takes place due to two types of policy decisions where this classification is done according to intensity of attrition, it form an ordinary renewal process. Assuming (i) policy decisions and exits occur at different epochs (ii) wastage of manpower due to exits and wastage due to frequent breaks taken by the personnel working in the manpower system separately form a sequence of independent and identically distributed exponential random variables with different means and (iii) breakdown threshold for the cumulative wastage of manpower in the system has three components which are independent exponential random variables. A stochastic model is constructed and the variance of the time to recruitment is obtained using an univariate CUM policy of recruitment. Employing a different probabilistic analysis, analytical results in closed form for system characteristics are derived.

DETERMINATION OF VARIANCE OF TIME TO RECRUITMENT WITH INTER-DECISION TIME AS GEOMETRIC PROCESS WHEN THE THRESHOLD HAS THREE COMPONENTS

In this paper, the problem of time to recruitment is analyzed for a single grade manpower system using an univariate CUM policy of recruitment. Assuming policy decisions and exits occur at different epochs, wastage of manpower due to exits form a sequence of independent and identically distributed exponential random variables, the inter-decision times form a geometric process and inter-exist time form an independent and identically distributed random variable. The breakdown threshold for the cumulative wastage of manpower in the system has three components which are independent exponential random variables. Employing a different probabilistic analysis, analytical results in closed form for system characteristics are derived

A new trivariate model for stochastic episodes

We study the joint distribution of stochastic events described by (X,Y,N), where N has a 1-inflated (or deflated) geometric distribution and X, Y are the sum and the maximum of N exponential random variables. Models with similar structure have been used in several areas of applications, including actuarial science, finance, and weather and climate, where such events naturally arise. We provide basic properties of this class of multivariate distributions of mixed type, and discuss their applications. Our results include marginal and conditional distributions, joint integral transforms, moments and related parameters, stochastic representations, estimation and testing. An example from finance illustrates the modeling potential of this new model.

Exponential and Hypoexponential Distributions: Some Characterizations

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some n≥2, X1,X2,…,Xn are independent copies of a random variable X with unknown distribution F and a specific linear combination of Xj’s has hypoexponential distribution, then F is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently by Arnold and Villaseñor (2013) for a particular convolution of two random variables.

A new approach for arriving at higher frequencies through stochastic modelling: application to site attenuation (kappa)

<p>We propose a framework for stochastically modelling the Fourier spectrum of the noisy seismic recording, considering that a seismic signal is a random rather than a deterministic quantity. We show that under this assumption, the noisy recording’s periodogram can be modelled as independent Exponential random variables with a frequency-dependent mean. With this model, estimating seismological parameters can be tackled through Maximum Likelihood (ML), allowing a fast, accurate and robust solution. This new approach constitutes a general estimation framework applicable to any parameter estimation that uses spectral analysis. Here we apply it to the high-frequency decay parameter kappa, which is particularly important for estimating and adjusting ground motion on rock. The improved ML performance is shown through a series of experiments on synthetic and recorded seismograms. The biggest advantage of the new method is its ability to account for the noise in the recording instead of just trying to avoid it, as is typically done when any ‘acceptable’ frequency range is isolated through signal-to-noise (SNR) criteria. As a result, our proposed technique can achieve acceptable results even for what would be typically considered very low and often unusable SNR, pushing the boundary of what is considered usable quality in seismic recordings.</p>