scholarly journals Exact Distributions of Sequential Threshold Estimators

1998 ◽  
pp. 126-137
Author(s):  
Nancy Flournoy ◽  
Douglas G. Kelly
Keyword(s):  
Exact Distributions ◽  
Threshold Estimators

scholarly journals Rate of convergence for traditional Pólya urns

2020 ◽  
Vol 57 (4) ◽  
pp. 1029-1044
Author(s):  
Svante Janson
Keyword(s):  
Rate Of Convergence ◽  
Dirichlet Distribution ◽  
Fixed Number ◽  
Kolmogorov Distance ◽  
Initial Composition ◽  
Exact Distributions ◽  
Polya Urn ◽  
The One ◽  
Lévy Distance ◽  
Direct Calculations

AbstractConsider a Pólya urn with balls of several colours, where balls are drawn sequentially and each drawn ball is immediately replaced together with a fixed number of balls of the same colour. It is well known that the proportions of balls of the different colours converge in distribution to a Dirichlet distribution. We show that the rate of convergence is $\Theta(1/n)$ in the minimal $L_p$ metric for any $p\in[1,\infty]$, extending a result by Goldstein and Reinert; we further show the same rate for the Lévy distance, while the rate for the Kolmogorov distance depends on the parameters, i.e. on the initial composition of the urn. The method used here differs from the one used by Goldstein and Reinert, and uses direct calculations based on the known exact distributions.

Exact distributions of constrained (k, ℓ) strings of failures between subsequent successes

2012 ◽  
Vol 54 (3) ◽  
pp. 783-806 ◽  
Author(s):  
Frosso S. Makri ◽  
Zaharias M. Psillakis
Keyword(s):  
Exact Distributions

BLOCK AND BASU'S BIVARIATE EXPONENTIAL DISTRIBUTION WITH APPLICATION TO DROUGHT DATA

2006 ◽  
Vol 21 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Exponential Distribution ◽  
Bivariate Exponential Distribution ◽  
Bivariate Exponential ◽  
Exact Distributions ◽  
Hydrological Applications

Motivated by hydrological applications, the exact distributions ofR=X+Y,P=XY, andW=X/(X+Y) and the corresponding moment properties are derived whenXandYfollow Block and Basu's bivariate exponential distribution. An application of the results is provided to drought data from Nebraska.

Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

1983 ◽  
Vol 20 (1) ◽  
pp. 47-54 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib
Keyword(s):  
Plane Strain ◽  
Half Plane ◽  
Inclination Angle ◽  
Complex Variable ◽  
Earth Pressure ◽  
Exact Distributions ◽  
Exact Determination ◽  
Upper Half Plane ◽  
Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

scholarly journals Exact distributions for stochastic models of gene expression with arbitrary regulation

2019 ◽  
Vol 63 (3) ◽  
pp. 485-500 ◽  
Author(s):  
Zihao Wang ◽  
Zhenquan Zhang ◽  
Tianshou Zhou
Keyword(s):  
Gene Expression ◽  
Stochastic Models ◽  
Exact Distributions

Optimal Design of Reliability Acceptance Sampling Plan Based on Data Obtained from Partially Accelerated Life Test (PALT)

2019 ◽  
Vol 27 (02) ◽  
pp. 2040002
Author(s):  
M. Kumar ◽  
P. N. Bajeel ◽  
P. C. Ramyamol
Keyword(s):  
Weibull Distribution ◽  
Accelerated Life Test ◽  
Maximum Likelihood Estimates ◽  
Acceptance Sampling ◽  
Accelerated Life Tests ◽  
Acceptance Sampling Plan ◽  
Accelerated Life ◽  
Acceptance Sampling Plans ◽  
Exact Distributions ◽  
Life Tests

In this paper, constant–stress partially accelerated life tests (PALT) are considered for a product with the assumption that the lifetime of the product follows Weibull distribution with known shape parameter and unknown scale parameter. Based on data obtained using Type-II censoring, the maximum likelihood estimates (MLEs) of the Weibull parameters and acceleration factor are obtained assuming linear and Arrhenius relationships with the lifetime characteristics and stress. Exact distributions of the MLEs of the parameters of Weibull distribution are also obtained. Optimal acceptance sampling plans are developed using both linear and Arrhenius relationships. Some numerical results are also presented to illustrate the resulted test plans.

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