Exponential distribution likelihood

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SUMMARY

This discussion focuses on handling censored data within the context of exponential distribution likelihood functions. Specifically, it addresses a scenario where three observations are made, with the third observation being censored at x3 > 10. The correct approach to formulate the likelihood function for the parameter lambda involves using the known observations and the cumulative distribution function (CDF) for the censored value, resulting in the likelihood function f(5) * f(3) * (1 - F(10)). This method ensures accurate estimation despite the missing data.

PREREQUISITES
  • Understanding of exponential distribution and its properties
  • Familiarity with likelihood functions and parameter estimation
  • Knowledge of censored data and its implications in statistical analysis
  • Proficiency in using cumulative distribution functions (CDF)
NEXT STEPS
  • Study the derivation of likelihood functions for censored data
  • Learn about maximum likelihood estimation (MLE) techniques for exponential distributions
  • Explore statistical software tools for handling censored data, such as R or Python's SciPy library
  • Investigate advanced topics in survival analysis and its applications
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Statisticians, data analysts, and researchers dealing with censored data in exponential distributions, as well as anyone interested in likelihood estimation techniques.

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

do the likelihood function as follows:

f(5)*f(3)*(1 - F(10))
 

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