The more interesting results are as follows: \begin We also present a method to perform counterfactual analysis without the explosion of branching counterfactuals. The results have relevant implications for forecasting, dealing with model risk and generally all statistical analyses. Here we follow an alternative route, the epistemological one, using counterfactual analysis, and show how nested uncertainty, that is, errors on the error in estimation of parameters, lead to fattailedness of the distribution. Many mechanisms have been used to show the emergence of fat tails. This is an epistemological approach to errors in both inference and risk management, leading to necessary structural properties for the probability distribution. 370 Negative Binomial Distribution To calculate the variance of X, the follow-ingpropertyisused,whereYandZareinde-pendentvariables: Var (Y +Z) Var (Y)+Var (Z). where is the pdf of the negative Binomial distribution and hence the above statement is validated. The length is taken to be the number required.į(x) = Γ(r+x)/(x! Γ(r)) * B(α+r, β+x) / B(α, β)Ĭumulative distribution function is calculated using recursive algorithm that employs the fact that Logical if TRUE (default), probabilities are P Logical if TRUE, probabilities p are given as log(p). Non-negative parameters of the beta distribution. Must be strictly positive, need not be integer. Results: In this paper, we propose a Zero-inflated Negative Binomial (ZINB) regression for identifying differentially abundant taxa between two or more populations.
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