# Exponential distribution likelihood

• Merka
In summary, when dealing with missing data in an exponential distribution, we can use the likelihood function f(5)*f(3)*(1 - F(10)) to account for the censored data. This allows us to still estimate the parameter lambda for the distribution.
Merka
In general what do you do when some kind of data is missing from some data that follows exponential distribution. For example, say 3 observations are made by an instrument where x1=5, x2=3, but for x3 the instrument can not give a specific answer because it can't measure past 10. So the only info we have about x3 is that x3>10. How can we come up with a likelihood function of lambda for this data (which is exponential distributed)? do we just use x3=10, or what?

This is censored data (since we know there were 3 observations):

do the likelihood function as follows:

f(5)*f(3)*(1 - F(10))

## 1. What is the Exponential distribution likelihood?

The Exponential distribution likelihood is a probability distribution used to model continuous random variables that measure the time between events. It is commonly used to model the waiting time between occurrences of a Poisson process.

## 2. How is the Exponential distribution likelihood calculated?

The Exponential distribution likelihood is calculated using the formula: f(x) = λ * e^(-λx), where λ is the rate parameter and x is the observed time. This formula represents the probability density function (PDF) of the Exponential distribution.

## 3. What is the role of the rate parameter in the Exponential distribution likelihood?

The rate parameter, denoted by λ, determines the shape and scale of the Exponential distribution. It represents the average number of events occurring per unit of time and is used to calculate the probability of an event occurring in a specific time interval.

## 4. What are the key properties of the Exponential distribution likelihood?

The Exponential distribution likelihood has several key properties, including: 1) It is a continuous probability distribution, 2) It is a one-parameter distribution, 3) It has a long right tail, and 4) The mean and standard deviation of the distribution are equal to the inverse of the rate parameter, 1/λ.

## 5. In what real-life situations is the Exponential distribution likelihood commonly used?

The Exponential distribution likelihood is commonly used to model the time between events in a variety of real-life situations, such as: 1) The lifespan of electronic components, 2) The time between arrivals of customers at a service counter, 3) The time between failures of a machine, and 4) The time between earthquakes or other natural disasters.

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