Abstract
A new log location-scale regression model with applications to voltage and Stanford heart transplant data sets is presented and studied. The martingale and modified deviance residuals to detect outliers and evaluate the model assumptions are defined. The new model can be very useful in analysing and modeling real data and provides more better fits than other regression models such as the log odd log-logistic generalized half-normal, the log beta generalized half-normal, the log generalized half-normal, the log-Topp-Leone odd log- logistic-Weibull and the log-Weibull models. Characterizations based on truncated moments as well as in terms of the reverse hazard function are presented. The maximum likelihood method is discussed to estimate the model parameters by means of a graphical Monte Carlo simulation study. The flexibility of the new model illustrated by means of four real data sets.
Highlights
Let Y1, ... , Yn, ... be a sequence of independent and identically distributed random variables with common cumulative distribution function, F(y)
The new log-location regression model based on the Odd log-logistic Fréchet (OLLFr) distribution provides better fits than log OLL generalized half-normal, log beta generalized half-normal, log generalized half-normal, log Topp-Leone odd log-logistic-Weibull and log-Weibull models for voltage and Stanford heart transplant data sets
Based on the residual analysis for the new log-location regression model, we conclude that none of the observed values appear as possible outliers as well as based on the index plot of the modified deviance residual and the Q-Q plot for modified deviance residual we note that OLLFr model is more appropriate for voltage and Stanford heart transplant data sets than all the existing regression models
Summary
Let Y1, ... , Yn, ... be a sequence of independent and identically distributed random variables (iid rv’s) with common cumulative distribution function (cdf ), F(y). We are motivated to introduce the OLLFr distribution because it contains a number aforementioned known lifetime models as sub models like the OLL inverse exponential (OLLIE) model when b = 1 and the OLL inverse Rayleigh model (OLLIR) when b = 2 It is shown that the OLLFr distribution can be expressed as a double linear mixture of Fr densities It can be viewed as a suitable model for fitting the right-skewed and symmetric data sets. The new log-location regression model based on the OLLFr distribution provides better fits than log OLL generalized half-normal, log beta generalized half-normal, log generalized half-normal, log Topp-Leone odd log-logistic-Weibull and log-Weibull models for voltage and Stanford heart transplant data sets.
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