Exponential Distribution Calculator

Understand the exponential distribution calculator result

Exponential Distribution Calculator gives a focused calculation for modeling a memoryless wait such as time between idealized independent events. It asks for rate lambda, waiting time x and reports density and cumulative probability and survival probability. For a constant event rate, survival is e to negative lambda x, the CDF is one minus survival, and density is lambda times survival. At rate 0.5 and time 2, the model places about 63.21 percent of waits at or below two. By exposing density and cumulative probability and survival probability, Exponential Distribution Calculator makes this specific arithmetic inspectable instead of presenting an unexplained number.

With the page defaults of Rate lambda 0.5, Waiting time x 2, the verified output is Density 0.1839397, Cumulative probability 0.6321206, Survival probability 0.3678794. Rate and time must be reciprocal units, such as events per hour with hours. In Exponential Distribution Calculator, each labeled default remains visible while you edit, so you can change one assumption at a time and trace how density responds.

Method, limits, and private processing

Real waiting processes may have changing rates and therefore violate the exponential assumption. Exponential Distribution Calculator evaluates the entered values entirely in your browser, without sending the inputs to a server. When using its density and cumulative probability and survival probability, retain the stated method and input units because this result is bounded by the assumptions of for a constant event rate, survival is e to negative lambda x, the CDF is one minus survival, and density is lambda times survival.