Application of Probability Distributions to Model Patient Waiting Time at Federal Medical Centre Yola

Patient waiting time is a key determinant of healthcare quality perception and service efficiency, and its statistical characterisation enables evidence-based queue management improvements at Nigerian tertiary hospitals. This study applies probability distribution fitting to model patient waiting time at the Federal Medical Centre, Yola, Adamawa State, North East Nigeria. Waiting times were recorded for 400 outpatient visits at the general outpatient department over a four-week period, covering registration wait, triage wait, and physician consultation wait. Empirical distributions were fitted to exponential, log-normal, and Weibull theoretical distributions using maximum likelihood estimation. Goodness-of-fit was assessed by Kolmogorov-Smirnov tests and Akaike Information Criterion. Descriptive statistics showed a mean total waiting time of 87 minutes with a standard deviation of 54 minutes and a positive skew of 2.1. The log-normal distribution provided the best fit to total waiting time (KS statistic = 0.062, p = 0.18; AIC = 3,412). Registration wait was best modelled by the exponential distribution. Probability estimates showed that 34 percent of patients waited more than two hours and 12 percent waited more than three hours. Waiting times were significantly longer on Mondays and on clinic days with over 80 registered patients. The study provides a probability-based waiting time characterisation for FMC Yola and recommends appointment scheduling optimisation and triage staff augmentation during peak volume periods. Keywords: waiting time, probability distribution, outpatient, Federal Medical Centre Yola, queue modelling