Joint Distributions of Numbers of Success-Runs and Failures Until the First Consecutive k Successes in a Binary Sequence

1997 ◽  
Vol 49 (3) ◽  
pp. 519-529 ◽  
Author(s):  
N. Balakrishnan
Keyword(s):  
Binary Sequence ◽  
Success Runs ◽  
Joint Distributions

Lengths of runs and waiting time distributions by using Pólya-Eggenberger sampling scheme

2002 ◽  
Vol 39 (3-4) ◽  
pp. 309-332 ◽  
Author(s):  
K. Sen ◽  
Manju L. Agarwal ◽  
S. Chakraborty
Keyword(s):  
Waiting Time ◽  
Lattice Path ◽  
Sampling Scheme ◽  
Bernoulli Trials ◽  
Success Runs ◽  
Waiting Time Distributions ◽  
Joint Distributions ◽  
First Occurrence

In this paper, joint distributions of number of success runs of length k and number of failure runs of length k' are obtained by using combinatorial techniques including lattice path approach under Pólya-Eggenberger model. Some of its particular cases, for different values of the parameters, are derived. Sooner and later waiting time problems and joint distributions of number of success runs of various types until first occurrence of consecutive success runs of specified length under the model are obtained. The sooner and later waiting time problems for Bernoulli trials (see Ebneshahrashoob and Sobel [3]) and joint distributions of the type discussed by Uchiada and Aki [11] are shown as particular cases. Assuming Ln and Sn to be the lengths of longest and smallest success runs, respectively, in a sample of size n drawn by Pólya-Eggenberger sampling scheme, the joint distributions of Ln and  Sn as well as distribution of M=max(Ln,Fn)n, where Fn is the length of longest failure run, are also  obtained.

Assessing joint distributions with isoprobability contours

2009 ◽  
Author(s):  
David V. Budescu ◽  
Ali E. Abbas ◽  
Yuhong Gu
Keyword(s):  
Joint Distributions

Efficient Steganography Algorithm Based On DCT And Entropy Thresholding Technique

2018 ◽  
Vol 8 (1) ◽  
pp. 45
Author(s):  
Satvir Singh
Keyword(s):  
Relative Entropy ◽  
Experimental Work ◽  
Random Function ◽  
Signal To Noise Ratio ◽  
Binary Sequence ◽  
Threshold Value ◽  
Absolute Difference ◽  
Secret Message ◽  
Signal To Noise ◽  
Confidential Information

Steganography is the special art of hidding important and confidential information in appropriate multimedia carrier. It also restrict the detection of  hidden messages. In this paper we proposes steganographic method based on dct and entropy thresholding technique. The steganographic algorithm uses random function in order to select block of the image where the elements of the binary sequence of a secret message will be inserted. Insertion takes place at the lower frequency  AC coefficients of the  block. Before we insert the secret  message. Image under goes dc transformations after insertion of the secret message we apply inverse dc transformations. Secret message will only be inserted into a particular block if  entropy value of that particular block is greater then threshold value of the entropy and if block is selected by the random function. In  Experimental work we calculated the peak signal to noise ratio(PSNR), Absolute difference , Relative entropy. Proposed algorithm give high value of PSNR  and low value of Absolute difference which clearly indicate level of distortion in image due to insertion of secret message is reduced. Also value of  relative entropy is close to zero which clearly indicate proposed algorithm is sufficiently secure. 

Sign in / Sign up

Export Citation Format

Share Document