A recursive algorithm to generate joint probability distribution of arrivals from exponential sources during a random time interval

1982 ◽  
Vol 14 (5) ◽  
pp. 214-217 ◽  
Author(s):  
J.G. Shanthikumar
Keyword(s):  
Probability Distribution ◽  
Recursive Algorithm ◽  
Joint Probability ◽  
Random Time ◽  
Joint Probability Distribution ◽  
Time Interval ◽  
Random Time Interval

Statistical Analysis for the Duration and Time Intervals of Tropical Cyclones, Hong Kong

2019 ◽  
Author(s):  
Shanshan Tao ◽  
Jialing Song ◽  
Zhifeng Wang ◽  
Yong Liu ◽  
Sheng Dong
Keyword(s):  
Hong Kong ◽  
Tropical Cyclone ◽  
Probability Distribution ◽  
Tropical Cyclones ◽  
Conditional Probability ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Time Interval ◽  
Time Intervals

Abstract Hong Kong is impacted by tropical cyclones from April to December each year. The duration of tropical cyclones is one key factor to impact the normal operation of port or coastal engineering, and longer time interval between two tropical cyclones can provide longer operation or construction time. Therefore, it is quite important to study on the long-term laws of the duration and time intervals of tropical cyclones which attacked Hong Kong. The Hong Kong Observatory issues the warning signals to warn the public of the threat of winds associated with a tropical cyclone. Choose the tropical cyclones with warning signal No. 3 or above as the research object. A statistical study was conducted on the duration of each tropical cyclone, the time interval between every two continuous tropical cyclones during the year, and the time interval between the last cyclone of each year and the first cyclone of the following year. Poisson compound extreme value distributions are constructed to calculate the return values, which can make people know how long a tropical cyclone with a fixed duration or time interval occurs once in statistical average sense. Based on bivariate copulas, the joint probability distribution of duration and time intervals of tropical cyclones are presented. Then when the duration of a tropical cyclone is known, the conditional probability that the time interval before the next tropical cyclone occurs is greater than a certain value can be calculated. The results provide corresponding conditional probability distributions. Similarly, for the sum of the duration of tropical cyclones each year, and the time interval between the last cyclone of each year and the first cyclone of the following year, their joint probability distribution and conditional probability distributions are also presented. The conditional probability can provide the probabilistic prediction of the length of the stationary period (with no impact of tropical cyclones).

scholarly journals Perishable Inventory System with Postponed Demands and Negative Customers

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Paul Manuel ◽  
B. Sivakumar ◽  
G. Arivarignan
Keyword(s):  
Steady State ◽  
Joint Probability ◽  
Inventory System ◽  
Arrival Process ◽  
Inventory Level ◽  
Joint Probability Distribution ◽  
Time Interval ◽  
Negative Customers ◽  
Perishable Inventory System ◽  
Number Of Customers

This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP). The lifetime of items in the stock and the lead time of reorder are assumed to be independently distributed as exponential. Demands that occur during the stock-out periods either enter a pool which has capacity N(<∞) or are lost. Any demand that takes place when the pool is full and the inventory level is zero is assumed to be lost. The demands in the pool are selected one by one, if the replenished stock is above s, with time interval between any two successive selections distributed as exponential with parameter depending on the number of customers in the pool. The waiting demands in the pool independently may renege the system after an exponentially distributed amount of time. In addition to the regular demands, a second flow of negative demands following MAP is also considered which will remove one of the demands waiting in the pool. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are calculated and the total expected cost per unit time is also considered. The results are illustrated numerically.

scholarly journals The Degree Analysis of an Inhomogeneous Growing Network with Two Types of Vertices

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Huilin Huang
Keyword(s):  
Probability Distribution ◽  
Law Of Large Numbers ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Degree Sequences ◽  
Strong Law ◽  
Large Numbers ◽  
Different Types ◽  
Azuma's Inequality ◽  
Growing Network

We consider an inhomogeneous growing network with two types of vertices. The degree sequences of two different types of vertices are investigated, respectively. We not only prove that the asymptotical degree distribution of typesfor this process is power law with exponent2+1+δqs+β1-qs/αqs, but also give the strong law of large numbers for degree sequences of two different types of vertices by using a different method instead of Azuma’s inequality. Then we determine asymptotically the joint probability distribution of degree for pairs of adjacent vertices with the same type and with different types, respectively.

Improved Locality Preserving Projection for Hyperspectral Image Classification in Probabilistic Framework

2021 ◽  
Author(s):  
Reza Seifi Majdar ◽  
Hassan Ghassemian
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Spatial Information ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Spectral Features ◽  
Probabilistic Framework ◽  
Locality Preserving ◽  
Training Samples

Unlabeled samples and transformation matrix are two main parts of unsupervised and semi-supervised feature extraction (FE) algorithms. In this manuscript, a semi-supervised FE method, locality preserving projection in the probabilistic framework (LPPPF), to find a sufficient number of reliable and unmixed unlabeled samples from all classes and constructing an optimal projection matrix is proposed. The LPPPF has two main steps. In the first step, a number of reliable unlabeled samples are selected based on the training samples, spectral features, and spatial information in the probabilistic framework. In this way, the spectral and spatial probability distribution function is calculated for each unlabeled sample. Therefore, the spectral features and spatial information are integrated together with a joint probability distribution function. Finally, a sufficient number of unlabeled samples with the highest joint probability distribution are selected. In the second step, the selected unlabeled samples are applied to construct the transformation matrix based on the spectral and spatial information of the unlabeled samples. The adjacency graph is improved by using new weights based on spectral and spatial information. This method is evaluated on three data sets: Indian Pines, Pavia University, and Kennedy Space Center (KSC) and compared with some recent and well-known supervised, semi-supervised, and unsupervised FE methods. Various experiments demonstrate the efficiency of the LPPPF in comparison with the other FE methods. LPPPF has also considerable performance with limited training samples.

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