= Random relabelling is not independent right censoring
Suppose the recorded durations retain an <exponential distribution> of rate $\theta$, but an independent fraction $q$ are relabelled as failures and the rest as <right-censored>. Applying the ordinary <survival likelihood> gives $\widehat\theta=d/\sum_i y_i\to q\theta$, rather than $\theta$. A censoring flag chosen independently of the recorded duration does not establish <independent censoring> of a latent failure time. Genuine simulation instead draws an event time and an independent censoring time and records their minimum.
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