TY - JOUR
T1 - A Review of the Rayleigh Distribution
T2 - Properties, Estimation & Application to COVID-19 Data
AU - Anis, M. Z.
AU - Okorie, I. E.
AU - Ahsanullah, M.
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.
PY - 2024/1
Y1 - 2024/1
N2 - We study the different properties of the Rayleigh distribution. These include the descriptive properties, reliability properties and stochastic orders. Next, we consider seven different estimation methods for estimating the parameter, namely: maximum likelihood estimation, matching moments estimation, maximum product of spacing estimation, ordinary least squares estimation, Cramér-von Mises estimation, Anderson-Darling estimation and right-tail Anderson-Darling estimation. A simulation study is done to assess the performance of these methods of estimation and the results shows that all the estimators are mostly efficient and consistent. Finally, using the method of maximum likelihood estimation, we demonstrate the applicability of the Rayleigh distribution by modelling the Netherlands’s COVID-19 mortality rate data as an example.
AB - We study the different properties of the Rayleigh distribution. These include the descriptive properties, reliability properties and stochastic orders. Next, we consider seven different estimation methods for estimating the parameter, namely: maximum likelihood estimation, matching moments estimation, maximum product of spacing estimation, ordinary least squares estimation, Cramér-von Mises estimation, Anderson-Darling estimation and right-tail Anderson-Darling estimation. A simulation study is done to assess the performance of these methods of estimation and the results shows that all the estimators are mostly efficient and consistent. Finally, using the method of maximum likelihood estimation, we demonstrate the applicability of the Rayleigh distribution by modelling the Netherlands’s COVID-19 mortality rate data as an example.
KW - Estimation methods
KW - Moments
KW - Reliability functions
KW - Statistical properties
UR - http://www.scopus.com/inward/record.url?scp=85176097983&partnerID=8YFLogxK
U2 - 10.1007/s40840-023-01605-z
DO - 10.1007/s40840-023-01605-z
M3 - Article
AN - SCOPUS:85176097983
SN - 0126-6705
VL - 47
JO - Bulletin of the Malaysian Mathematical Sciences Society
JF - Bulletin of the Malaysian Mathematical Sciences Society
IS - 1
M1 - 6
ER -