(Basic Statistics for Citizen Data Scientist)
The exponential distribution can be used to determine the probability that it will take a given number of trials to arrive at the first success in a Poisson distribution; i.e. it describes the inter-arrival times in a Poisson process. It is the continuous counterpart to the geometric distribution, and it too is memoryless.
Definition 1: The exponential distribution has probability density function (pdf) given by
Excel Function: Excel provides the following function for the exponential distribution:
EXPONDIST(x, λ, cum) where λ is the parameter in Definition 1 and cum = TRUE or FALSE
EXPONDIST(x, λ, FALSE) = f(x) where f is the pdf value at x as defined above
EXPONDIST(x, λ, TRUE) = F(x) where F is the cumulative distribution function value at x corresponding to f above
In Excel 2010, 2013 and 2016 there is the additional function EXPON.DIST which is equivalent to EXPONDIST.
Observation: The exponential distribution is equivalent to the gamma distribution with α = 1 and β = 1/λ. Thus, EXPONDIST(x, λ, cum) = GAMMADIST(x, 1, 1/λ, cum).
There is no EXPON.INV(p, λ) function in Excel, but GAMMA.INV(p, 1, 1/λ) or –LN(1–p)/λ or the following Real Statistics function can be used instead.
Real Statistics Function: The Real Statistics Resource Pack supplies the following function.
EXPON_INV(p, λ) = the inverse of the exponential distribution at p
The cumulative distribution function is
Other key statistical properties are:
- Mean = 1 / λ
- Median = ln 2/λ
- Mode = 0
- Range = [0, ∞)
- Variance = 1 / λ2
- Skewness = 2
- Kurtosis = 6
How to do Damped Trend Linear Exponential Smoothing model using lynx dataset – Time Series Forecasting
Statistics for Beginners in Excel – Exponential Distribution
Disclaimer: The information and code presented within this recipe/tutorial is only for educational and coaching purposes for beginners and developers. Anyone can practice and apply the recipe/tutorial presented here, but the reader is taking full responsibility for his/her actions. The author (content curator) of this recipe (code / program) has made every effort to ensure the accuracy of the information was correct at time of publication. The author (content curator) does not assume and hereby disclaims any liability to any party for any loss, damage, or disruption caused by errors or omissions, whether such errors or omissions result from accident, negligence, or any other cause. The information presented here could also be found in public knowledge domains.
Learn by Coding: v-Tutorials on Applied Machine Learning and Data Science for Beginners
Latest end-to-end Learn by Coding Projects (Jupyter Notebooks) in Python and R:
All Notebooks in One Bundle: Data Science Recipes and Examples in Python & R.
End-to-End Python Machine Learning Recipes & Examples.
End-to-End R Machine Learning Recipes & Examples.
Applied Statistics with R for Beginners and Business Professionals
Data Science and Machine Learning Projects in Python: Tabular Data Analytics
Data Science and Machine Learning Projects in R: Tabular Data Analytics
Python Machine Learning & Data Science Recipes: Learn by Coding
R Machine Learning & Data Science Recipes: Learn by Coding
Comparing Different Machine Learning Algorithms in Python for Classification (FREE)
There are 2000+ End-to-End Python & R Notebooks are available to build Professional Portfolio as a Data Scientist and/or Machine Learning Specialist. All Notebooks are only $29.95. We would like to request you to have a look at the website for FREE the end-to-end notebooks, and then decide whether you would like to purchase or not.