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positive as well as negative values, but duration by its very nature cannot be negative
and therefore normality cannot be assumed when dealing with duration/survival data.
Hence the normality assumption of regression models is violated.
The assumption is that if the data were not censored it would be representative of the
population of interest. In survival analysis, censored observations arise whenever the
dependent variable of interest represents the time to a terminal event, and the duration
of the study is limited in time.
An important concept in survival analysis is the hazard rate, defined as the probability
that the event will occur at time t conditional on surviving until time t. Another concept
related to the hazard rate is the survival function which can be defined as the probability
of surviving t[he] time.
Most models try to model the hazard rate by choosing the underlying distribution
depending on the shape of the hazard function. A distribution whose hazard function
slopes upward is said to have positive duration dependence, a decreasing hazard
shows negative duration dependence whereas constant hazard is a process with no
memory usually characterized by the exponential distribution.
Some of the distributional choices in survival models are: F, gamma, Weibull, log
normal, inverse normal, exponential etc. All these distributions are for a non-negative
random variable.
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