What Is the Exponential Distribution Calculator?
An exponential distribution calculator models continuous time intervals between random Poisson events.
How Does the Exponential Distribution Calculator Work?
Evaluates continuous exponential functions e^(-λx) to compute cumulative and survival probabilities.
Exponential Distribution Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
F(x) = 1 - e^(-λx) · S(x) = e^(-λx) · Mean = 1 ÷ λ
Evaluates the exponential CDF for probability of event occurring before x, and the survival function for probability of exceeding x.
How to Use the Exponential Distribution Calculator
- Input event rate λ and target elapsed time interval x.
Step-by-Step Example Calculation
Rate λ = 0.5 with interval x = 2
Input Values:
rateLambda:0.5
timeX:2
Understanding Your Result
Shows probability of event occurring within time x, probability of exceeding x, and mean waiting duration.
Factors That Affect the Result
- Rate parameter λ directly dictates scale and decay speed.
When Should You Use This Calculator?
- Electronics component lifespan modeling, radioactive decay half-lives, service queue waiting times, and customer service arrival intervals.
Assumptions & Limitations
- Assumes constant failure or arrival rate over time.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Exact continuous exponential analysis.