Mixture of Two LindleyProbability Models And Application In Reliability

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Ehtesham Husain ◽  
Masood Ul Haq
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Mixture Model ◽  
Mathematical Expectation ◽  
Probability Distributions ◽  
Reliability Function ◽  
Probability Models ◽  
Probability Functions ◽  
Two Component ◽  
In Series

<span>Mixture probability models are developed in general<br /><span>from Uni variate Probability functions (say)<br /><span><em>g</em><span>1 <span>(<span><em>x</em><span>) <span><em>and g</em><span>2 <span>(<span><em>x</em><span>) <span>. The mixture of these two is defined by<br /><span><em>f</em><span>(<span><em>x</em><span>)  <span><em>p</em><span>.<span><em>g</em><span>1 <span>(<span><em>x</em><span>)  (1  <span><em>p</em><span>) <span><em>g</em><span>2 <span>(<span><em>x</em><span>) <span>where “p” is the mixing<br /><span>ratio. The function that we have in the present paper is the<br /><span>Mixture of two Lindley probability distributions, each of<br /><span>which is having a different parameter. Lindley models are<br /><span>also useful for data showing decaying trends. The properties<br /><span>of Lindley probability distribution that have been shown<br /><span>are Mathematical Expectation, Second Moment, and the<br /><span>Distribution Function. An application of the Mixture Model<br /><span>which has been derived in the present research , has been<br /><span>applied to the Reliability function , in a two component<br /><span>system , when the components are connected in series. The<br /><span>Reliability of the discussed system is compared with<br /><span>reliability values when the Lindley probabilities in the same<br /><span>system , are independent.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /><br class="Apple-interchange-newline" /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>

Conditional Mixture Model for Correlated Neuronal Spikes

2010 ◽  
Vol 22 (7) ◽  
pp. 1718-1736 ◽  
Author(s):  
Shun-ichi Amari
Keyword(s):  
Probability Distribution ◽  
Mixture Models ◽  
Mixture Model ◽  
Computational Neuroscience ◽  
General Model ◽  
Probability Distributions ◽  
Real Data ◽  
Spike Trains ◽  
Cell Assemblies ◽  
Competitive Model

Analysis of correlated spike trains is a hot topic of research in computational neuroscience. A general model of probability distributions for spikes includes too many parameters to be of use in analyzing real data. Instead, we need a simple but powerful generative model for correlated spikes. We developed a class of conditional mixture models that includes a number of existing models and analyzed its capabilities and limitations. We apply the model to dynamical aspects of neuron pools. When Hebbian cell assemblies coexist in a pool of neurons, the condition is specified by these assemblies such that the probability distribution of spikes is a mixture of those of the component assemblies. The probabilities of activation of the Hebbian assemblies change dynamically. We used this model as a basis for a competitive model governing the states of assemblies.

scholarly journals Rainfall models – a study over Gangtok

MAUSAM ◽  
2021 ◽  
Vol 61 (2) ◽  
pp. 225-228
Author(s):  
K. SEETHARAM
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Uniform Distribution ◽  
Probability Distribution Function ◽  
Null Hypothesis ◽  
Probability Distributions ◽  
Data Sets ◽  
Type I ◽  
Anderson Darling ◽  
Pearsonian Type

In this paper, the Pearsonian system of curves were fitted to the monthly rainfalls from January to December, in addition to the seasonal as well as annual rainfalls totalling to 14 data sets of the period 1957-2005 with 49 years of duration for the station Gangtok to determine the probability distribution function of these data sets. The study indicated that the monthly rainfall of July and summer monsoon seasonal rainfall did not fit in to any of the Pearsonian system of curves, but the monthly rainfalls of other months and the annual rainfalls of Gangtok station indicated to fit into Pearsonian type-I distribution which in other words is an uniform distribution. Anderson-Darling test was applied to for null hypothesis. The test indicated the acceptance of null-hypothesis. The statistics of the data sets and their probability distributions are discussed in this paper.

scholarly journals Establishment of a Stochastic Model for Sustainable Economic Flood Management in Yewa Sub-Basin, Southwest Nigeria

2016 ◽  
Vol 2 (12) ◽  
pp. 646-655 ◽  
Author(s):  
O.A Agbede ◽  
Oluwatobi Aiyelokun
Keyword(s):  
Probability Distribution ◽  
Stochastic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Flood Management ◽  
Return Periods ◽  
Probability Models ◽  
Goodness Of Fit Test ◽  
Southwest Nigeria ◽  
Anderson Darling

Of all natural disasters, floods have been considered to have the greatest potential damage. The magnitude of economic damages and number of people affected by flooding have recently increased globally due to climate change. This study was based on the establishment of a stochastic model for reducing economic floods risk in Yewa sub-basin, by fitting maximum annual instantaneous discharge into four probability distributions. Daily discharge of River Yewa gauged at Ijaka-Oke was used to establish a rating curve for the sub-basin, while return periods of instantaneous peak floods were computed using the Hazen plotting position. Flood magnitudes were found to increase with return periods based on Hazen plotting position. In order to ascertain the most suitable probability distribution for predicting design floods, the performance evaluation of the models using root mean square error was employed. In addition, the four probability models were subjected to goodness of fit test besed on Anderson-Darling (A2) and Kolmogorov-Smirnov (KS). As a result of the diagnostics test the Weibul probability distribution was confirmed to fit well with the empirical data of the study area. The stochastic model  generated from the Weibul probability distribution, could be used to enhance sustainable development by reducing economic flood damages in the sub-basin.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

scholarly journals Two-Component Mixture Model in the Presence of Covariates

2021 ◽  
pp. 1-15 ◽  
Author(s):  
Nabarun Deb ◽  
Sujayam Saha ◽  
Adityanand Guntuboyina ◽  
Bodhisattva Sen
Keyword(s):  
Mixture Model ◽  
Component Mixture ◽  
Two Component

scholarly journals An Online Application for ΔR Calculation

Radiocarbon ◽  
2016 ◽  
Vol 59 (5) ◽  
pp. 1623-1627 ◽  
Author(s):  
Ron W Reimer ◽  
Paula J Reimer
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Calibration Curve ◽  
Probability Distribution Function ◽  
Museum Collections ◽  
Online Program ◽  
Online Application ◽  
Radiocarbon Calibration

AbstractA regional offset (ΔR) from the marine radiocarbon calibration curve is widely used in calibration software (e.g. CALIB, OxCal) but often is not calculated correctly. While relatively straightforward for known-age samples, such as mollusks from museum collections or annually banded corals, it is more difficult to calculate ΔR and the uncertainty in ΔR for 14C dates on paired marine and terrestrial samples. Previous researchers have often utilized classical intercept methods that do not account for the full calibrated probability distribution function (pdf). Recently, Soulet (2015) provided R code for calculating reservoir ages using the pdfs, but did not address ΔR and the uncertainty in ΔR. We have developed an online application for performing these calculations for known-age, paired marine and terrestrial 14C dates and U-Th dated corals. This article briefly discusses methods that have been used for calculating ΔR and the uncertainty and describes the online program deltar, which is available free of charge.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

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