Some inferences on a mixture of exponential and Rayleigh distributions based on fuzzy data

Abstract

PurposeIn this paper, a mixture of exponential and Rayleigh distributions in the proportions α and 1 − α and all the parameters in the mixture distribution are estimated based on fuzzy data.Design/methodology/approachThe methods such as maximum likelihood estimation (MLE) and method of moments (MOM) are applied for estimation. Fuzzy data of triangular fuzzy numbers and Gaussian fuzzy numbers for different sample sizes are considered to illustrate the resulting estimation and to compare these methods. In addition to this, the obtained results are compared with existing results for crisp data in the literature.FindingsThe application of fuzziness in the data will be very useful to obtain precise results in the presence of vagueness in data. Mean square errors (MSEs) of the resulting estimators are computed using crisp data and fuzzy data. On comparison, in terms of MSEs, it is observed that maximum likelihood estimators perform better than moment estimators.Originality/valueClassical methods of obtaining estimators of unknown parameters fail to give realistic estimators since these methods assume the data collected to be crisp or exact. Normally, such case of precise data is not always feasible and realistic in practice. Most of them will be incomplete and sometimes expressed in linguistic variables. Such data can be handled by generalizing the classical inference methods using fuzzy set theory.

Optimal Variable Acceptance Sampling Plan under Progressive Type-II Censoring for Mixture Distribution: Applications in Breast Cancer Data

“…Statistical analysis addresses such complexities by employing mixture distributions, combining two or more component distributions to create a more comprehensive model for failure events. Muralidharan and Lathika (2005) introduced a mixture of exponential-Rayleigh distributions and compared the estimators of the parameters obtained via MLE and the method of moments. Some of the other studies in the parameter inference can be seen in (Mendenhall and Hader, 1958;Muralidharan, 2000;Muralidharan and Lathika, 2006;Mathai and Kumar, 2023).…”

“…Muralidharan and Lathika (2005) introduced a mixture of exponential-Rayleigh distributions and compared the estimators of the parameters obtained via MLE and the method of moments. Some of the other studies in the parameter inference can be seen in (Mendenhall and Hader, 1958;Muralidharan, 2000;Muralidharan and Lathika, 2006;Mathai and Kumar, 2023). Despite the significance of mixture distributions in several practical statistical areas, variable acceptance sampling plans (ASPs) for mixed distributions are not well addressed in the literature.…”