Folded Skewed Type ? Generalized Logistic Distribution

Folded distribution was mainly studied in the 1960 s,and the most famous one is the folded normal distribution In 1961,Leone proposed an estimation method forthe parameters of the folded normal distribution by using moment estimation,and studied the properties of the folded normal distribution.After that,psarakis folded the t distribution for the first time,and derived the folded t distribution.It is worth mentioning that cooray obtained the folded logistic distribution by folding the logistic distribution at the mean in 2006,and gave the relevant methods of parameter estimation.Because several different forms of generalized logistic distributions have been proposed in the past literature,these distributions are called generalized logistic distribution.There are four types of generalized logistic distribution:type I,type II,type ? and type IV.Johnson gave the definition of type ? generalized logistic distribution in 1995.Theodossiou introduced skewed type ? generalized logistic distribution on the basis of type ? generalized logistic distribution according to the idea of different left-right deviation.This paper introduces a new folded skewed type ? generalized logistic distribution.This distribution is folded based on skewed type ? generalized logistic distribution.Compared with skewed type ? generalized logistic distribution,it has thickertails and is more suitable for data with thicker tails.Firstly,we discuss the influence of the parameters on the density function curve of the folded skewed type ? generalized logistic distribution.The parameter K affects the kurtosis and the tail thickness of the folded skewed type ? generalized logistic distribution,and has a positive correlation with the kurtosis and a negative correlation with the tail thickness.The parameter ? affects the offset degree of the folded skewed type ? generalized logistic distribution,which is positively correlated with the offset degree.(?) affects the kurtosis and tail thickness of folded skewed type ? generalized logistic distribution,which is negatively correlated with kurtosis and positively correlated with tail thickness Secondly,we use the method of maximum likelihood estimation to preliminarily estimate the parameters of folded skewed type ? generalized logistic distribution.In addition,because the parameters of folded skewed type ? generalized logistic distribution are too many and unstable in the process of parameter solution,the parameters are obtained in turn by the method of dimension reduction iteration.At the end of the paper,we use the lamp life data as an application example.Firstly,we study the distribution of bulb life data.The histogram of bulb life data shows that the data has some similar characteristics of normal distribution,but its skewness and kurtosis data do not conform to normal distribution.We confirm that the bulb life data does not conform to normal distribution through skewness test and has the characteristics of peak and thick tail.Secondly,we study the survival distribution of bulb life.We choose to discuss the survival distribution of bulb life when the life is greater than 690 and 695,and use the dimension reduction iteration method to obtain the parameter estimation of folded skewed type ? generalized logic distribution.