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Waiting time at transit stops is found to be an influential policy variable for a passenger's decision on whether to undertake a given transit service. With regard to policy framework for improvement of operational service headway of a transit service and thereby its waiting time, the necessity to have knowledge on its critical value becomes inevitable. The critical value of waiting time for passengers waiting at transit stops is that duration beyond which passengers are found to be no more interested to wait for a that transit service. The paper demonstrates an approach for estimating the critical value of waiting time at urban transit stops with reference to public transport services such as city bus and shared-auto operational in Bhubaneswar, India. The critical value of waiting time is estimated from the point on cumulative distribution curve of waiting time frequency distribution, at which the maximum rate of change of the slope of curve occurs. The work assumes two positively skewed distributions such as gamma and log-normal for observed distributional pattern of waiting time. The work identifies that gamma distribution is comparatively fitting the observed data better than log-normal distribution. The study reveals that the critical value of waiting time for city bus passengers is about twice than that of shared auto passengers. Though, the study presents new information on critical values of waiting time with reference to an urban area of a developing country, it also demonstrates an experience on application of probability distribution functions for understanding distributional pattern of waiting time.