TY - JOUR
T1 - Representative Points from a Mixture of Two Normal Distributions
AU - Li, Yinan
AU - Fang, Kai Tai
AU - He, Ping
AU - Peng, Heng
N1 - Our work was supported in part by the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College (2022B1212010006) and in part by the Internal Research Grant (R202010) of BNU-HKBU United International College.
Publisher Copyright:
© 2022 by the authors.
PY - 2022/11
Y1 - 2022/11
N2 - In recent years, the mixture of two-component normal distributions (MixN) has attracted considerable interest due to its flexibility in capturing a variety of density shapes. In this paper, we investigate the problem of discretizing a MixN by a fixed number of points under the minimum mean squared error (MSE-RPs). Motivated by the Fang-He algorithm, we provide an effective computational procedure with high precision for generating numerical approximations of MSE-RPs from a MixN. We have explored the properties of the nonlinear system used to generate MSE-RPs and demonstrated the convergence of the procedure. In numerical studies, the proposed computation procedure is compared with the k-means algorithm. From an application perspective, MSE-RPs have potential advantages in statistical inference.Our numerical studies show that MSE-RPs can significantly improve Kernel density estimation.
AB - In recent years, the mixture of two-component normal distributions (MixN) has attracted considerable interest due to its flexibility in capturing a variety of density shapes. In this paper, we investigate the problem of discretizing a MixN by a fixed number of points under the minimum mean squared error (MSE-RPs). Motivated by the Fang-He algorithm, we provide an effective computational procedure with high precision for generating numerical approximations of MSE-RPs from a MixN. We have explored the properties of the nonlinear system used to generate MSE-RPs and demonstrated the convergence of the procedure. In numerical studies, the proposed computation procedure is compared with the k-means algorithm. From an application perspective, MSE-RPs have potential advantages in statistical inference.Our numerical studies show that MSE-RPs can significantly improve Kernel density estimation.
KW - Fang-He algorithm
KW - k-means algorithm
KW - Kernel density estimations
KW - mixture of normal distributions
KW - representative points
UR - http://www.scopus.com/inward/record.url?scp=85141875350&partnerID=8YFLogxK
U2 - 10.3390/math10213952
DO - 10.3390/math10213952
M3 - Journal article
AN - SCOPUS:85141875350
SN - 2227-7390
VL - 10
JO - Mathematics
JF - Mathematics
IS - 21
M1 - 3952
ER -