scholarly journals A STOCHASTIC MODEL FOR ESTIMATION OF EXPECTED TIME TO RECRUITMENT WHEN THE THRESHOLD HAS GENERALIZED EXPONENTIATED GAMMA DISTRIBUTION

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 20-27
Author(s):  
Manoharan M ◽  
◽  
Rajarathinam A ◽  
Keyword(s):  
Stochastic Model ◽  
Gamma Distribution ◽  
Random Variable ◽  
Threshold Level ◽  
Random Time ◽  
Numerical Examples ◽  
Time Points ◽  
Expected Time ◽  
Number Of Factors ◽  
Vital Factor

In any organization a number of factors are required to generate production activities and the manpower is the most vital factor. The manpower requirements may increase in course of time due to increase in production activities or due to depletion of manpower at random time points. Hence recruitment is to be made whenever the total demands for manpower crosses the so called threshold level. In this paper an estimate of the expected time to recruitment is derived under the assumption that the threshold level is a random variable which follows the Generalized Exponentiated Gamma distribution. The variances also found out. The results are substantiated with numerical examples

scholarly journals An Optimal Tail Selection in Risk Measurement

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 70
Author(s):  
Małgorzata Just ◽  
Krzysztof Echaust
Keyword(s):  
Mean Squared Error ◽  
Real Data ◽  
Random Variable ◽  
Threshold Level ◽  
Middle Part ◽  
Risk Measurement ◽  
Practical Applications ◽  
Tuning Parameters ◽  
Path Stability ◽  
Asymptotic Mean Squared Error

The appropriate choice of a threshold level, which separates the tails of the probability distribution of a random variable from its middle part, is considered to be a very complex and challenging task. This paper provides an empirical study on various methods of the optimal tail selection in risk measurement. The results indicate which method may be useful in practice for investors and financial and regulatory institutions. Some methods that perform well in simulation studies, based on theoretical distributions, may not perform well when real data are in use. We analyze twelve methods with different parameters for forty-eight world indices using returns from the period of 2000–Q1 2020 and four sub-periods. The research objective is to compare the methods and to identify those which can be recognized as useful in risk measurement. The results suggest that only four tail selection methods, i.e., the Path Stability algorithm, the minimization of the Asymptotic Mean Squared Error approach, the automated Eyeball method with carefully selected tuning parameters and the Hall single bootstrap procedure may be useful in practical applications.

A semi-hybrid model for malaria with limited superinfection

1998 ◽  
Vol 30 (04) ◽  
pp. 1027-1057 ◽  
Author(s):  
Philippe Picard
Keyword(s):  
Stochastic Model ◽  
Population Size ◽  
Hybrid Model ◽  
Human Population ◽  
Threshold Level ◽  
The Other ◽  
The Difference ◽  
The One

Modelling malaria with consistency necessitates the introduction of at least two families of interconnected processes. Even in a Markovian context the simplest fully stochastic model is intractable and is usually transformed into a hybrid model, by supposing that these two families are stochastically independent and linked only through two deterministic connections. A model closer to the fully stochastic model is presented here, where one of the two families is subordinated to the other and just a unique deterministic connection is required. For this model a threshold theorem can be proved but the threshold level is not the one obtained in a hybrid model. The difference disappears only when the human population size approaches infinity.

scholarly journals Concordance Modeling With a Gold Standard for Variables From the Three-Parameter Gamma Distribution

2020 ◽  
Vol 8 (2) ◽  
pp. 284
Author(s):  
Márcio Paulo de Oliveira ◽  
Miguel Angel Uribe-Opazo ◽  
Manuel Galea ◽  
Jerry Adriani Johann
Keyword(s):  
Gamma Distribution ◽  
Gold Standard ◽  
Weather Forecasting ◽  
Geographical Location ◽  
Random Variable ◽  
Climatic Data ◽  
Weather Forecasts ◽  
Rainfall Forecast ◽  
Environmental Prediction ◽  
Range Interval

A way to compare two or more measurements for the same random variable can be achieved by using a negligible error reference measurement, which is called the gold standard, obtained by consolidated measurement methods. This paper presents a new methodology for comparing measurements in the presence of a gold standard with random variables from the multivariate three-parameter (shape, scale, and location) gamma distribution. The errors between gold standard measures and approximate measures have a gamma difference distribution with the same three parameters of the gamma distribution. The concordance measurements were obtained by mean of a coefficient, which measures the degree of agreement as a ratio between the variances of the gold standard and the errors. The developed methodology is illustrated with climatic data which is divided into four ranges. The measurements analyzed are rainfall forecasts of the following four national centers: Canadian Meteorological Center (CMC), European Center for Medium-Range Weather Forecasts (ECMWF), National Centers for Environmental Prediction (NCEP), and Center for Weather Forecasting and Climate Studies (CPTEC). The forecast range was 240 hours for the West mesoregion of Paraná – Brazil, and in the October 1–March 31 period of the 2010/2011 –2015/2016 harvest years. The period was selected because it is related to soybean crop development in the region and because several crop estimation models use rainfall forecast data in this period. The methodology applied spatially indicated the center to be selected in each geographical location according to each rainfall range interval. The gamma model fit well with the data and is an alternative to the normal one for modelling rainfall, in particular to estimate concordances between rainfall forecasts and the gold standard, which are used to improve the selection of rainfall forecast centers.

Conditioned limit theorems for waiting-time processes of the M/G/1 queue

1983 ◽  
Vol 20 (03) ◽  
pp. 675-688 ◽  
Author(s):  
G. Hooghiemstra
Keyword(s):  
Waiting Time ◽  
Limit Theorems ◽  
Random Variable ◽  
Weak Limit ◽  
Random Time ◽  
Time Process ◽  
Brownian Excursion ◽  
Time Index ◽  
Waiting Time Process ◽  
Number Of Customers

This paper is on conditioned weak limit theorems for imbedded waiting-time processes of an M/G/1 queue. More specifically we study functional limit theorems for the actual waiting-time process conditioned by the event that the number of customers in a busy period exceeds n or equals n. Attention is also paid to the actual waiting-time process with random time index. Combined with the existing literature on the subject this paper gives a complete account of the conditioned limit theorems for the actual waiting-time process of an M/G/1 queue for arbitrary traffic intensity and for a rather general class of service-time distributions. The limit processes that occur are Brownian excursion and meander, while in the case of random time index also the following limit occurs: Brownian excursion divided by an independent and uniform (0, 1) distributed random variable.

On population-size-dependent branching processes

1984 ◽  
Vol 16 (1) ◽  
pp. 30-55 ◽  
Author(s):  
F. C. Klebaner
Keyword(s):  
Stochastic Model ◽  
Asymptotic Behaviour ◽  
Rate Of Convergence ◽  
Population Size ◽  
Gamma Distribution ◽  
Branching Processes ◽  
Independent Random Variables ◽  
Size Dependent ◽  
Offspring Distribution ◽  
The Mean

We consider a stochastic model for the development in time of a population {Zn} where the law of offspring distribution depends on the population size. We are mainly concerned with the case when the mean mk and the variance of offspring distribution stabilize as the population size k grows to ∞, The process exhibits different asymptotic behaviour according to m < l, m = 1, m> l; moreover, the rate of convergence of mk to m plays an important role. It is shown that if m < 1 or m = 1 and mn approaches 1 not slower than n–2 then the process dies out with probability 1. If mn approaches 1 from above and the rate of convergence is n–1, then Zn/n converges in distribution to a gamma distribution, moreover a.s. both on a set of non-extinction and there are no constants an, such that Zn/an converges in probability to a non-degenerate limit. If mn approaches m > 1 not slower than n–α, α > 0, and do not grow to ∞ faster than nß, β <1 then Zn/mn converges almost surely and in L2 to a non-degenerate limit. A number of general results concerning the behaviour of sums of independent random variables are also given.

scholarly journals Austenite Grain Size Estimtion from Chord Lengths of Logarithmic-Normal Distribution

2017 ◽  
Vol 62 (4) ◽  
pp. 2015-2019
Author(s):  
H. Adrian ◽  
K. Wiencek
Keyword(s):  
Grain Size ◽  
Normal Distribution ◽  
Gamma Distribution ◽  
Interval Estimation ◽  
Random Variable ◽  
Point Estimation ◽  
Size Estimation ◽  
Present Contribution ◽  
Austenite Grain Size ◽  
The One

AbstractLinear section of grains in polyhedral material microstructure is a system of chords. The mean length of chords is the linear grain size of the microstructure. For the prior austenite grains of low alloy structural steels, the chord length is a random variable of gamma- or logarithmic-normal distribution. The statistical grain size estimation belongs to the quantitative metallographic problems. The so-called point estimation is a well known procedure. The interval estimation (grain size confidence interval) for the gamma distribution was given elsewhere, but for the logarithmic-normal distribution is the subject of the present contribution. The statistical analysis is analogous to the one for the gamma distribution.

A note on fire frequency concepts and definitions

2006 ◽  
Vol 36 (7) ◽  
pp. 1884-1888 ◽  
Author(s):  
William J Reed
Keyword(s):  
Random Variable ◽  
Fire Frequency ◽  
Current Form ◽  
Fire Cycle ◽  
Expected Time ◽  
Time Required

The concepts of hazard of burning, fire interval, and fire cycle are considered. It is claimed that the current notion of fire cycle is poorly defined, since the time required to burn a specified area is a random variable. It is shown that the expected time to burn an area equal in size to the study area normally exceeds the fire interval (the average time between fires at any location). In view of this, it is recommended that the notion of fire cycle in its current form be abandoned.

Does Network Theory Contradict Trait Theory?

2012 ◽  
Vol 26 (4) ◽  
pp. 447-448 ◽  
Author(s):  
Rolf Steyer
Keyword(s):  
Stochastic Process ◽  
Network Theory ◽  
Latent Variable ◽  
Random Variable ◽  
Time Points ◽  
Trait Theory ◽  
Colloquial Language

I argue that the trait and network theories of personality are not necessarily contradictory. If appropriately formalized, it may turn out that network theory incorporates traits as part of the theory. I object the opinion that if a trait is a cause of behaviour, then it is necessarily an entity operating in the minds of individuals. Finally, I argue that liking parties can be a label for a random variable (item), a stochastic process (a family of items at different time points) and a latent variable (trait). In our colloquial language, we do not make these distinctions, which leads often to confusions. Copyright © 2012 John Wiley & Sons, Ltd.

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