scholarly journals An improved exact sampling algorithm for the standard normal distribution

2021 ◽  
Author(s):  
Yusong Du ◽  
Baoying Fan ◽  
Baodian Wei
Keyword(s):  
Normal Distribution ◽  
Standard Normal Distribution ◽  
Sampling Algorithm ◽  
Exact Sampling ◽  
Standard Normal

scholarly journals A New Linear Regression Kalman Filter with Symmetric Samples

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2139
Author(s):  
Xiuqiong Chen ◽  
Jiayi Kang ◽  
Mina Teicher ◽  
Stephen S.-T. Yau
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Particle Filter ◽  
Normal Distribution ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Unscented Kalman Filter ◽  
Standard Normal Distribution ◽  
Leibler Divergence ◽  
Standard Normal

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

The computation of standard normal distribution integral in any required precision based on reliability method

2018 ◽  
Vol 48 (6) ◽  
pp. 1517-1528
Author(s):  
Yuge Dong ◽  
Haimeng Zhang ◽  
Liangguo He ◽  
Can Wang ◽  
Minghui Wang
Keyword(s):  
Normal Distribution ◽  
Standard Normal Distribution ◽  
Reliability Method ◽  
Standard Normal

scholarly journals Mendel’s pea crosses: varieties, traits and statistics

Hereditas ◽  
2019 ◽  
Vol 156 (1) ◽  
Author(s):  
T. H. Noel Ellis ◽  
Julie M. I. Hofer ◽  
Martin T. Swain ◽  
Peter J. van Dijk
Keyword(s):  
Statistical Analysis ◽  
Normal Distribution ◽  
Standard Normal Distribution ◽  
Data Sets ◽  
Crossing Experiments ◽  
Independent Variables ◽  
F2 Population ◽  
A Value ◽  
Segregation Ratios ◽  
Standard Normal

Abstract A controversy arose over Mendel’s pea crossing experiments after the statistician R.A. Fisher proposed how these may have been performed and criticised Mendel’s interpretation of his data. Here we re-examine Mendel’s experiments and investigate Fisher’s statistical criticisms of bias. We describe pea varieties available in Mendel’s time and show that these could readily provide all the material Mendel needed for his experiments; the characters he chose to follow were clearly described in catalogues at the time. The combination of character states available in these varieties, together with Eichling’s report of crosses Mendel performed, suggest that two of his F3 progeny test experiments may have involved the same F2 population, and therefore that these data should not be treated as independent variables in statistical analysis of Mendel’s data. A comprehensive re-examination of Mendel’s segregation ratios does not support previous suggestions that they differ remarkably from expectation. The χ2 values for his segregation ratios sum to a value close to the expectation and there is no deficiency of extreme segregation ratios. Overall the χ values for Mendel’s segregation ratios deviate slightly from the standard normal distribution; this is probably because of the variance associated with phenotypic rather than genotypic ratios and because Mendel excluded some data sets with small numbers of progeny, where he noted the ratios “deviate not insignificantly” from expectation.

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