scholarly journals An Efficient Polynomial Approximation to the Normal Distribution Function and Its Inverse Function

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Winston A. Richards ◽  
Robin S ◽  
Ashok Sahai ◽  
M. Raghunadh Acharya
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Polynomial Approximation ◽  
Inverse Function ◽  
Normal Distribution Function

scholarly journals Copulaesque Versions of the Skew-Normal and Skew-Student Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 815
Author(s):  
Christopher Adcock
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Degrees Of Freedom ◽  
Special Functions ◽  
Normal Distribution Function ◽  
Skew Normal Distribution ◽  
Marginal Distributions ◽  
Student’S T ◽  
Normal Copula ◽  
Skew Normal

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples.

scholarly journals An Improved Ship Collision Risk Evaluation Method for Korea Maritime Safety Audit Considering Traffic Flow Characteristics

2019 ◽  
Vol 7 (12) ◽  
pp. 448 ◽  
Author(s):  
Yunja Yoo ◽  
Tae-Goun Kim
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Traffic Flow ◽  
Evaluation Method ◽  
Collision Probability ◽  
Normal Distribution Function ◽  
Collision Risk ◽  
Ship Traffic ◽  
Ship Collision ◽  
Best Fit

Ship collision accidents account for the majority of marine accidents. The collision risk can be even greater in ports where the traffic density is high and terrain conditions are difficult. The proximity assessment model of the Korea Maritime Safety Audit (KMSA), which is a tool for improving maritime traffic safety, employs a normal distribution of ship traffic to calculate the ship collision risk. However, ship traffic characteristics can differ according to the characteristics of the sea area and shipping route. Therefore, this study simulates collision probabilities by estimating the best-fit distribution function of ship traffic flow in Ulsan Port, which is the largest hazardous cargo vessel handling port in Korea. A comparison of collision probability simulation results using the best-fit function and the normal distribution function reveals a difference of approximately 1.5–2.4 times for each route. Moreover, the collision probability estimates are not accurate when the normal distribution function is uniformly applied without considering the characteristics of each route. These findings can be used to improve the KMSA evaluation method for ship collision risks, particularly in hazardous port areas.

Normal-distribution-function-shaped Josephson tunnel junctions

2000 ◽  
Vol 77 (22) ◽  
pp. 3660-3661 ◽  
Author(s):  
Katsuya Kikuchi ◽  
Hiroaki Myoren ◽  
Takeshi Iizuka ◽  
Susumu Takada
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Tunnel Junctions ◽  
Normal Distribution Function ◽  
Josephson Tunnel ◽  
Josephson Tunnel Junctions

Normal distribution function shaped superconducting tunnel junctions with Ta electrodes

2002 ◽  
Vol 372-376 ◽  
pp. 395-398
Author(s):  
Hiroaki Myoren ◽  
Yuki Kogure ◽  
Ryo Abe ◽  
Katsuya Kikuchi ◽  
Takeshi Iizuka ◽  
...  
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Tunnel Junctions ◽  
Superconducting Tunnel Junctions ◽  
Normal Distribution Function

X-Ray Detection Using Superconducting Tunnel Junction Shaped Normal-Distribution-Function

2007 ◽  
Vol E90-C (3) ◽  
pp. 566-569 ◽  
Author(s):  
T. TAINO ◽  
T. NISHIHARA ◽  
K. HOSHINO ◽  
H. MYOREN ◽  
H. SATO ◽  
...  
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Tunnel Junction ◽  
Superconducting Tunnel Junction ◽  
Normal Distribution Function ◽  
X Ray

Saddlepoint approximations for bivariate distributions

1990 ◽  
Vol 27 (03) ◽  
pp. 586-597 ◽  
Author(s):  
Suojin Wang
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Normal Distribution ◽  
Cumulative Distribution Function ◽  
Saddlepoint Approximation ◽  
Monte Carlo Study ◽  
Cumulative Distribution ◽  
Normal Distribution Function ◽  
Sample Mean ◽  
Saddlepoint Approximations

A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

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