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As in the case of BNps, the ergodicy of the underlying Markov chain ensures the existence of the unique stationary distribution being the limiting distribution of the chain.
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The Tracy-Widom distribution is the limiting distribution for the largest eigenvalue of a covariance matrix having a central white Wishart distribution.
Using the set of these 100 highest-synergy scores, we obtained the maximum likelihood estimates of the location parameter and the scale parameter of the Gumbel (type-I extreme value) distribution, resulting in a cumulative density function F. The Gumbel distribution [ 43] is the limiting distribution of the maximum of a large number of random observations from the same arbitrary distribution.
In the limit of no discounting, Lemma 1 states that no matter which strategy player II is using, the limiting distribution v (if it exists) is on a hyperplane orthogonal to the difference of these two conditional probabilities.
Confidence intervals for the posterior probabilities of scenarios are computed through the limiting distribution of the maximum likelihood estimators.
A matrix recursive scheme is developed to determine the limiting distribution.
First of all, we establish the following result that is required to identify the limiting distribution of.
We show that the limiting distribution is non-standard and can be represented by a linear combination of independent normal and non-central chi-squared random variables.
Note that G ( x ) is the limit distribution of a 'residual waiting time' (see, Feller [6], p.368).
Note that G ( x ) is the limit distribution for the 'residual waiting time' generating by the sequence { ζ n } (see, Feller [6], p.386).
With the Chi square distribution as the limiting distribution, it is shown that 2NΔH is Chi square distributed.
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