A comparison of different parameter estimation methods for exponentially modified Gaussian distribution

The convolution of the independent Gaussian and exponential distribution is known as the exponentialy modified Gaussian (EMG) distribution. The main feature of this distribution is its differential behavior on the right and left tails. The distribution exhibits a normally-distributed left tail and an exponentially-distributed right tail. This distribution has found practical applications in a variety of scientific disciplines such as chromatography, cellular biology, radiotherapy, microarray preprocessing, and macroeconomics. With the precise measurement of different natural phenomena, fitting an appropriate distribution and estimation of its parameters is becoming challenging. This study discusses the complexity of parameter estimation of the EMG distribution. In particular, to estimate the parameters of the EMG, eleven different methods, namely the method of moment estimation (MME), approximated L-moment estimation (ALME), the maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), the maximum product spacing (MPS), the minimum spacing absolute distance estimation (MSADE), the minimum spacing absolute log-distance estimation (MSALDE), Cramer-Von-Mises (CVM), Anderson-Darling method (AD), and right-tail Anderson-Darling method (RAD) are considered. Besides a comprehensive simulation study, a real data on time in hours to detect cancer cells using 3um erlotinib is also a part of this study.