scholarly journals Estimating the Return to Endogenous Schooling Decisions for Australian Workers Via Conditional Second Moments

2006 ◽  
Author(s):  
Francis Vella ◽  
Roger W. Klein
Keyword(s):  
Schooling Decisions ◽  
Second Moments ◽  
Endogenous Schooling

scholarly journals Independently Controlling Stochastic Field Realization Magnitude and Phase Statistics for the Construction of Novel Partially Coherent Sources

Photonics ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 60
Author(s):  
Milo W. Hyde
Keyword(s):  
Coherent Beam ◽  
Optical Field ◽  
Stochastic Field ◽  
Partially Coherent ◽  
Second Moments ◽  
Coherent Beams ◽  
Gaussian Statistics ◽  
Simulated Field ◽  
Gaussian Moment ◽  
Partially Coherent Beams

In this paper, we present a method to independently control the field and irradiance statistics of a partially coherent beam. Prior techniques focus on generating optical field realizations whose ensemble-averaged autocorrelation matches a specified second-order field moment known as the cross-spectral density (CSD) function. Since optical field realizations are assumed to obey Gaussian statistics, these methods do not consider the irradiance moments, as they, by the Gaussian moment theorem, are completely determined by the field’s first and second moments. Our work, by including control over the irradiance statistics (in addition to the CSD function), expands existing synthesis approaches and allows for the design, modeling, and simulation of new partially coherent beams, whose underlying field realizations are not Gaussian distributed. We start with our model for a random optical field realization and then derive expressions relating the ensemble moments of our fields to those of the desired partially coherent beam. We describe in detail how to generate random optical field realizations with the proper statistics. We lastly generate two example partially coherent beams using our method and compare the simulated field and irradiance moments theory to validate our technique.

scholarly journals On the Accuracy of the Generalized Gamma Approximation to Generalized Negative Binomial Random Sums

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1571
Author(s):  
Irina Shevtsova ◽  
Mikhail Tselishchev
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Law Of Large Numbers ◽  
Negative Binomial ◽  
Infinite Divisibility ◽  
Random Sums ◽  
Generalized Gamma ◽  
Second Moments ◽  
Large Numbers ◽  
Generalized Negative Binomial Distribution

We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence in the Rényi theorem. In particular, we derive upper bounds for the Kantorovich and the Kolmogorov metrics in the law of large numbers for negative binomial random sums of i.i.d. random variables with nonzero first moments and finite second moments. Our method is based on the representation of the generalized negative binomial distribution with the shape and exponent power parameters no greater than one as a mixed geometric law and the infinite divisibility of the negative binomial distribution.

Stochastic control for risk under deregulated electricity market — a case study using a new formulation

2005 ◽  
Vol 32 (4) ◽  
pp. 719-725 ◽  
Author(s):  
Joyce Li Zhang ◽  
K Ponnambalam
Keyword(s):  
Electricity Market ◽  
Explicit Method ◽  
State Variables ◽  
Risk Minimization ◽  
Solution Approach ◽  
Second Moments ◽  
Deregulated Electricity Market ◽  
New Formulation ◽  
Dual Dynamic Programming

This paper describes the implementation of a new solution approach — Fletcher-Ponnambalam model (FP) — for risk management in hydropower system under deregulated electricity market. The FP model is an explicit method developed for the first and second moments of the storage state distributions in terms of moments of the inflow distributions. This method provides statistical information on the nature of random behaviour of the system state variables without any discretization and hence suitable for multi-reservoir problems. Also avoiding a scenario-based optimization makes it computationally inexpensive, as there is little growth to the size of the original problem. In this paper, the price uncertainty was introduced into the FP model in addition to the inflow uncertainty. Lake Nipigon reservoir system is chosen as the case study and FP results are compared with the stochastic dual dynamic programming (SDDP). Our studies indicate that the method could achieve optimum operations, considering risk minimization as one of the objectives in optimization.Key words: reservoir operations, explicit method, uncertainty, stochastic programming, risk.

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