Markov Inequality

See also: The basics of probability theory introduction, Tchebysheffs Rule

The Markov Inequality gives some indication of the range of a distribution, in a similar way to Tchebysheff's rule. It states that for a non-negative random variable X with mean m:

for any constant k greater than m.

So, for example, for a random variable with mean 6, the probability of being greater than 20 is less than or equal to 6/20 = 30%.

Of course, being very general like Tchebysheff's rule, it makes a rather conservative statement. For most distributions, the probability is much smaller than m/k. For example:

 

Distribution with m=6

P(X ≥ 20)

Exponential(6)

3.6%

ChiSq(6)

0.3%

Gamma(2,3)

1%

Inverse Gaussian(6,l)

Max of 6.9%

Lognormal(6,s)

Max of 6.0%

Pareto(q,6(q  - 1)/q)

Max of 3.21%

 

Read on: Rank Order Correlation Coefficient

 


 

 

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