A note on the characterization of a U-shaped probability density function

1972 ◽  
Vol 9 (3) ◽  
pp. 684-685 ◽  
Author(s):  
P. Ghosh ◽  
D. N. Shanbhag
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Characteristic Property

In this note a characterization for a U-shaped probability density function is given using a well-known result for unimodal distributions due to Khinchine. As a corollary of this result, a characteristic property based on moments is found.

A note on the characterization of a U-shaped probability density function

1972 ◽  
Vol 9 (03) ◽  
pp. 684-685
Author(s):  
P. Ghosh ◽  
D. N. Shanbhag
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Characteristic Property

In this note a characterization for a U-shaped probability density function is given using a well-known result for unimodal distributions due to Khinchine. As a corollary of this result, a characteristic property based on moments is found.

Study on Determining Safety-Monitoring Index for Concrete Dam Based on Cloud Model

2012 ◽  
Vol 226-228 ◽  
pp. 1106-1110 ◽  
Author(s):  
Dong Qin ◽  
Xue Qin Zheng ◽  
Song Lin Wang
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cloud Model ◽  
Safety Monitoring ◽  
Monitoring Data ◽  
Concrete Dam ◽  
Deterministic Function ◽  
Monitoring Index

The paper, based on analyzing original monitoring data, employs forward and backward cloud algorithm in studying determining safety-monitoring index for concrete dam ,which integrates randomness and fuzziness into of qualitative concept of digital features. By means of above monitoring data, its digital characteristics can be easily transformed to the “quantitative-qualitative- quantitative” change. The final generated quantitative value constitutes the cloud diagram where each droplet demonstrates the characterization of raw monitoring data. At the same time, it also shows the randomness and fuzziness of monitored value. we can study out the safety monitoring indexes according to different remarkable levels by using the probability density function and deterministic function which completed by cloud algorithm. In the end, it is obtained with practice that this method is more suitable and reliability.

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