Smith's Exponential Distribution

Smith's Exponential Distribution models the likelihood of time between events, such as failures or arrivals, where events happen randomly but at a steady average rate. Think of it as describing how long you might wait for a bus that arrives unpredictably but on average every 10 minutes. The distribution expresses that short waiting times are more common, but longer waits are possible, decreasing in probability as waiting time increases. It is useful in fields like reliability, queuing theory, and survival analysis to predict the chance of an event occurring after a certain period, assuming the event’s occurrence is memoryless—meaning past events don't influence future ones.