scholarly journals Bounded size bias coupling: a Gamma function bound, and universal Dickman-function behavior

2014 ◽  
Vol 162 (3-4) ◽  
pp. 411-429 ◽  
Author(s):  
Richard Arratia ◽  
Peter Baxendale
Keyword(s):  
Gamma Function ◽  
Dickman Function ◽  
Size Bias ◽  
Bounded Size

ON THE INCOMPLETE GAMMA FUNCTION AND ITS NEUTRIX CONVOLUTION FOR NEGATIVE INTEGERS

2019 ◽  
Vol 10 (1) ◽  
pp. 30-51
Author(s):  
Mongkolsery Lin ◽  
◽  
Brian Fisher ◽  
Somsak Orankitjaroen ◽  
◽  
...  
Keyword(s):  
Gamma Function ◽  
Incomplete Gamma Function

q-Extension of the p-Adic Gamma Function. II

1982 ◽  
Vol 273 (1) ◽  
pp. 111 ◽  
Author(s):  
Neal Koblitz
Keyword(s):  
Gamma Function

Gamma Function and Its Functional Equations

Resonance ◽  
2021 ◽  
Vol 26 (3) ◽  
pp. 367-386
Author(s):  
Ritesh Goenka ◽  
Gopala Krishna Srinivasan
Keyword(s):  
Gamma Function ◽  
Functional Equations

scholarly journals A Synopsis Based Approach for Itemset Frequency Estimation over Massive Multi-Transaction Stream

2021 ◽  
Vol 16 (2) ◽  
pp. 1-30
Author(s):  
Guangtao Wang ◽  
Gao Cong ◽  
Ying Zhang ◽  
Zhen Hai ◽  
Jieping Ye
Keyword(s):  
Frequency Estimation ◽  
Frequent Itemsets ◽  
Frequent Itemset ◽  
Experimental Results ◽  
Closure Property ◽  
Frequent Itemset Mining ◽  
Itemset Mining ◽  
Minimum Value ◽  
Downward Closure ◽  
Bounded Size

The streams where multiple transactions are associated with the same key are prevalent in practice, e.g., a customer has multiple shopping records arriving at different time. Itemset frequency estimation on such streams is very challenging since sampling based methods, such as the popularly used reservoir sampling, cannot be used. In this article, we propose a novel k -Minimum Value (KMV) synopsis based method to estimate the frequency of itemsets over multi-transaction streams. First, we extract the KMV synopses for each item from the stream. Then, we propose a novel estimator to estimate the frequency of an itemset over the KMV synopses. Comparing to the existing estimator, our method is not only more accurate and efficient to calculate but also follows the downward-closure property. These properties enable the incorporation of our new estimator with existing frequent itemset mining (FIM) algorithm (e.g., FP-Growth) to mine frequent itemsets over multi-transaction streams. To demonstrate this, we implement a KMV synopsis based FIM algorithm by integrating our estimator into existing FIM algorithms, and we prove it is capable of guaranteeing the accuracy of FIM with a bounded size of KMV synopsis. Experimental results on massive streams show our estimator can significantly improve on the accuracy for both estimating itemset frequency and FIM compared to the existing estimators.

Some complete monotonicity properties for the -gamma function

2013 ◽  
Vol 219 (21) ◽  
pp. 10538-10547 ◽  
Author(s):  
V.B. Krasniqi ◽  
H.M. Srivastava ◽  
S.S. Dragomir
Keyword(s):  
Gamma Function ◽  
Complete Monotonicity ◽  
Monotonicity Properties

An inequality for the gamma function using the analogue of Bhattacharyya's inequality

1969 ◽  
Vol 1969 (1-2) ◽  
pp. 71-77
Author(s):  
B. Raja Rao ◽  
M. L. Garg
Keyword(s):  
Gamma Function
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