scholarly journals PENDUGAAN KOMPONEN PERIODIK FUNGSI INTENSITAS BERBENTUK FUNGSI PERIODIK KALI TREN LINEAR SUATU PROSES POISSON NON-HOMOGEN

2013 ◽  
Vol 12 (1) ◽  
pp. 49
Author(s):  
W. ISMAYULIA ◽  
I W. MANGKU ◽  
S. SISWANDI
Keyword(s):  
Poisson Process ◽  
Mean Square Error ◽  
Linear Trend ◽  
Periodic Component ◽  
Mean Square ◽  
Homogeneous Poisson Process ◽  
Single Realization ◽  
The Mean ◽  
Bias Variance ◽  
Non Homogeneous Poisson Process

In this manuscript, estimation of the periodic component of intensity having form periodic function multiplied by the linear trend of a non homogeneous Poisson process is discussed. The estimator is constructed using a single realization of the Poisson process observed in the interval  0,𝑛 . It is assumed that the period of the periodic component is known. The convergence of the Mean Square Error (MSE) of the estimator has been proved. In addition, asymptotic approximations to the bias, variance, and Mean Square Error (MSE) of the estimator have been proved. An asymptotic optimal bandwidth is also given.

Mean-Square Convergence of Recursive Kernel Estimators of Non-Homogeneous Poisson Process Intensity Function and its Derivative

2015 ◽  
Vol 1084 ◽  
pp. 684-688
Author(s):  
Anna V. Kitaeva ◽  
Mikhail V. Kolupaev
Keyword(s):  
Poisson Process ◽  
Fixed Time ◽  
Kernel Estimators ◽  
Time Interval ◽  
Mean Square ◽  
Homogeneous Poisson Process ◽  
Single Realization ◽  
Mean Square Convergence ◽  
Scheme Of Series ◽  
Non Homogeneous Poisson Process

The structure of the estimators is similar to the recursive kernel estimators of a density function and its derivative. The estimators have been constructed using a single realization of Poisson process on a fixed time interval. Mean-square convergence has been proved in a scheme of series. Simulation studies have been carried out to illustrate the convergence.

scholarly journals Strong Consistency and Asymptotic Distribution of Estimator for the Intensity Function Having Form of Periodic Function Multiplied by Power Function Trend of a Poisson Process

2018 ◽  
Vol 8 (02) ◽  
Author(s):  
Nina Valentika ◽  
Wayan Mangku ◽  
Windiani Erliana
Keyword(s):  
Periodic Function ◽  
Poisson Process ◽  
Asymptotic Distribution ◽  
Power Function ◽  
Strong Consistency ◽  
Observation Interval ◽  
Intensity Function ◽  
Periodic Component ◽  
Single Realization ◽  
Non Homogeneous Poisson Process

This manuscript discusses the strong consistency and the asymptotic distribution of an estimator for a periodic component of the intensity function having a form of periodic function multiplied by power function trend of a non-homogeneous Poisson process by using a uniform kernel function. It is assumed that the period of the periodic component of intensity function is known. An estimator for the periodic component using only a single realization of a Poisson process observed at a certain interval has been constructed. This estimator has been proved to be strongly consistent if the length of the observation interval indefinitely expands. Computer simulation also showed the asymptotic normality of this estimator.

scholarly journals ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS

2005 ◽  
Vol 4 (1) ◽  
pp. 51
Author(s):  
I W. MANGKU ◽  
I. WIDIYASTUTI ◽  
I G. P. PURNABA
Keyword(s):  
Asymptotic Normality ◽  
Poisson Process ◽  
Power Function ◽  
Mean Squared Error ◽  
Asymptotic Bias ◽  
Inhomogeneous Poisson Process ◽  
Squared Error ◽  
Single Realization ◽  
The Mean ◽  
Bias Variance

<p>An estimator of the intensity in the form of a power function of an inhomogeneous Poisson process is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance and the mean- squared error of the proposed estimator are computed. Asymptotic normality of the estimator is also established.</p>

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

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