Estimation of Probability Distribution and Density Functions of Stochastic Process

2017 ◽  
pp. 487-522
Author(s):  
Vyacheslav Tuzlukov
Keyword(s):  
Stochastic Process ◽  
Probability Distribution ◽  
Density Functions

The Fast Diagonal-Matrix-Weight IMM Algorithm for Target Tracking

2012 ◽  
Vol 461 ◽  
pp. 132-137
Author(s):  
Yang Fu ◽  
Ming Wei ◽  
Hai Chuan Zhang ◽  
Liang Gao
Keyword(s):  
Stochastic Process ◽  
Computational Complexity ◽  
Target Tracking ◽  
Real Time ◽  
Probability Density Functions ◽  
Diagonal Matrix ◽  
Estimation Accuracy ◽  
Density Functions ◽  
Alternative Algorithm ◽  
Real Time Application

The diagonal-matrix-weight IMM (DIMM) algorithm can solve the IMM algorithm confusions of probability density functions (PDFs) and probability masses of stochastic process. Combingandfilter，the Fast-IMM algorithm has a better performance both in accuracy and reducing computational complexity. In order to improve the estimation accuracy and computational complexity，we apply Fast-IMM method to DIMM algorithm. Therefore，A new method, Fast diagonal-matrix-weight IMM (fast-DIMM) algorithm, is proposed in this paper to heighten the real-time application of DIMM algorithm. Simulations indicate that the proposed fast-DIMM algorithm is a competitive alternative algorithm to the IMM algorithm in real time application

The definition of a multi-dimensional generalization of shot noise

1971 ◽  
Vol 8 (01) ◽  
pp. 128-135 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Stochastic Process ◽  
Probability Distribution ◽  
Absolute Convergence ◽  
List Type ◽  
Type Number ◽  
Homogeneous Poisson Process ◽  
Cauchy Principal ◽  
Principal Value ◽  
Definition Of ◽  
Image Position

The paper studies the formally defined stochastic process where {tj } is a homogeneous Poisson process in Euclidean n-space En and the a.e. finite Em -valued function f(·) satisfies |f(t)| = g(t) (all |t | = t), g(t) ↓ 0 for all sufficiently large t → ∞, and with either m = 1, or m = n and f(t)/g(t) =t/t. The convergence of the sum at (*) is shown to depend on (i) (ii) (iii) . Specifically, finiteness of (i) for sufficiently large X implies absolute convergence of (*) almost surely (a.s.); finiteness of (ii) and (iii) implies a.s. convergence of the Cauchy principal value of (*) with the limit of this principal value having a probability distribution independent of t when the limit in (iii) is zero; the finiteness of (ii) alone suffices for the existence of this limiting principal value at t = 0.

scholarly journals Characterizations of Some Probability Distributions with Completely Monotonic Density Functions

2021 ◽  
pp. 51-64
Author(s):  
Mohammad Shakil ◽  
Dr. Mohammad Ahsanullah ◽  
Dr. B. M. G. Kibria Kibria
Keyword(s):  
Probability Distribution ◽  
Probability Density ◽  
Probability Distributions ◽  
Random Variable ◽  
Record Values ◽  
Density Functions ◽  
Exponential Distributions ◽  
Completely Monotonic ◽  
Percentage Points ◽  
Generalized Gamma Function

For a non-negative continuous random variable , Chaudhry and Zubair (2002, p. 19) introduced a probability distribution with a completely monotonic probability density function based on the generalized gamma function, and called it the Macdonald probability function. In this paper, we establish various basic distributional properties of Chaudhry and Zubair’s Macdonald probability distribution. Since the percentage points of a given distribution are important for any statistical applications, we have also computed the percentage points for different values of the parameter involved. Based on these properties, we establish some new characterization results of Chaudhry and Zubair’s Macdonald probability distribution by the left and right truncated moments, order statistics and record values. Characterizations of certain other continuous probability distributions with completely monotonic probability density functions such as Mckay, Pareto and exponential distributions are also discussed by the proposed characterization techniques.   

scholarly journals Convergence of estimated optimal inventory levels in models with probabilistic demands

2003 ◽  
Vol 13 (2) ◽  
pp. 217-227
Author(s):  
Carlos Bouza
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Search Algorithms ◽  
Inventory Level ◽  
Density Functions ◽  
Monte Carlo Experiments ◽  
Unknown Probability ◽  
Optimal Inventory Level

The behavior of estimations of the optimal inventory level is analyzed. Two models are studied. The demands follow unknown probability distribution function. The included density functions are estimated and a plug-in rule is suggested for computing estimates of the optimal levels. Two search algorithms are proposed and compared using Monte Carlo experiments. .

A Formal Specification of the Memorization Process

2011 ◽  
pp. 157-170
Author(s):  
Natalia López ◽  
Manuel Núñez ◽  
Fernando L. Pelayo
Keyword(s):  
Stochastic Process ◽  
Probability Distribution ◽  
Formal Specification ◽  
Cognitive Model ◽  
Distribution Functions ◽  
Cognitive Systems ◽  
Buffer Memory ◽  
Stochastic Time ◽  
Stochastic Process Algebra

In this chapter we present the formal language, stochastic process algebra (STOPA), to specify cognitive systems. In addition to the usual characteristics of these formalisms, this language features the possibility of including stochastic time. This kind of time is useful to represent systems where the delays are not controlled by fixed amounts of time, but are given by probability distribution functions. In order to illustrate the usefulness of our formalism, we will formally represent a cognitive model of the memory. Following contemporary theories of memory classification (see Squire et al., 1993; Solso, 1999) we consider sensory buffer, short-term, and long-term memories. Moreover, borrowing from Y. Wang and Y. Wang (2006), we also consider the so-called action buffer memory.

The Role Of Simulation And Modern Business Games

2011 ◽  
pp. 272-294
Author(s):  
Tamio Shimizu ◽  
Marley Monteiro de Carvalho ◽  
Fernando Jose Barbin
Keyword(s):  
Stochastic Process ◽  
Monte Carlo ◽  
Probability Distribution ◽  
Mathematical Models ◽  
Simple Game ◽  
Simulation Method ◽  
Average Value ◽  
Probabilistic Values ◽  
Modern Business ◽  
Probabilistic Process

“Probability or stochastic process” is a name used to designate mathematical models that represent the behavior of phenomena described by probability theory, ranging from a simple game of coin tossing up to more complex phenomenon like “Brownian motion theory”, “investment analysis”, etc. Stochastic process uses mathematical models to represent phenomena ruled by the probabilistic variation of some variable over time. Simulation methods, also known as Monte Carlo methods, are stochastic processes that use mathematical models that have similar behavior of real problems, feeding these models with random values generated according to some probability distribution. The term Monte Carlo is used as a synonym for simulation since in some problems the generation of probabilistic values was historically linked to the use of the roulette wheel. In this chapter we show how simulation method can be used to evaluate complex decision problems involving uncertainty. This kind of problem involves knowledge of probability distribution (such as uniform, Poisson, or Normal distribution) used to represent the probabilistic process and the value of respective parameters (such as the average value and the standard deviation). Simulation is the most appropriate tool for visualizing, testing, and evaluating the parameters and the dynamic behavior of a probabilistic process. Simulation uses algorithms that generate a population of probabilistic events which makes possible the estimation of the values of parameters of the problem. The results of a simulation can be proven to be valid approximations of the values of the real phenomenon which they simulate.

The definition of a multi-dimensional generalization of shot noise

1971 ◽  
Vol 8 (1) ◽  
pp. 128-135 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Stochastic Process ◽  
Probability Distribution ◽  
Absolute Convergence ◽  
List Type ◽  
Type Number ◽  
Homogeneous Poisson Process ◽  
Cauchy Principal ◽  
Principal Value ◽  
Definition Of ◽  
Image Position

The paper studies the formally defined stochastic process where {tj} is a homogeneous Poisson process in Euclidean n-space En and the a.e. finite Em-valued function f(·) satisfies |f(t)| = g(t) (all |t | = t), g(t) ↓ 0 for all sufficiently large t → ∞, and with either m = 1, or m = n and f(t)/g(t) =t/t. The convergence of the sum at (*) is shown to depend on (i)(ii)(iii). Specifically, finiteness of (i) for sufficiently large X implies absolute convergence of (*) almost surely (a.s.); finiteness of (ii) and (iii) implies a.s. convergence of the Cauchy principal value of (*) with the limit of this principal value having a probability distribution independent of t when the limit in (iii) is zero; the finiteness of (ii) alone suffices for the existence of this limiting principal value at t = 0.

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