A simple analogy for understanding blockchain technology is a Google Doc. When we create a document and share it with a group of people, the document is distributed instead of copied or transferred. This creates a decentralized distribution chain that gives everyone access to the document at the same time. No one is locked out awaiting changes from another party, while all modifications to the doc are being recorded in real-time, making changes completely transparent. Blockchain, sometimes referred to as Distributed Ledger Technology (DLT), makes the history of any digital asset unalterable and transparent through the use of decentralization and cryptographic hashing.
Data with excess zeros that uses the zero-inflated model assumes the outcome of the zeros is due to two different processes. The study data considered occurrence of death in Ghanaian female pensioners. the occurrence have two process; first that a pensioner death occurred which give a count outcome (non-zero death) and the second no death occurred which give a possible outcome of zero. The first part of the process which is the zeros is modeled by the logit whereas the negative binomial model is used to model the second part of the process which is the count. The expected count is expressed as a combination of the two processes;
E(n death occurrence = k) = P(no death)*0 + P(death)*E(y = k/death)
Zero inflated negative binomial distribution is a mixture of distribution which assign a amass of p to extra zeros and mass of (1 – p) to a negative binomial distribution , 0 ≤p ≤1 . it is a continuous mixture of Poisson distribution with mean μ o be gamma distributed and modeled the over dispersion. For better understanding of the zero-inflated negative binomial regression, review the negative binomial model;
P(Y = y) = (Γ (α +y))/(Γ (α) y !) (( μ)/(1+ β))^y (1/(1+ k μ))^α, y = 0, 1, 2, …;μ,α>0 3.10
Where μ = E(Y), α is the shape parameter which quantifies the amount of over dispersion and the response variable of interest is Y and the variance of Y is α + μ^2/α.. the ZINB distribution is given by
P(Y) = y) {█(p+(1-p) (1+ μ/α)^(- α), y=0@(1-p) (Γ (y+ α))/(y ! Γ (α)) (1+ α/μ)^(- y), y =1,2,… )┤ 3.11
The zero inflated negative binomial distribution has mean E(Y) = (1 – p) μ and variance to be Var (Y) = (1 – p) μ (1+pμ+ μ/α) , respectively. Note that the zero inflated negative binomial distribution reduces to Poisson distribution if both 1/α and p ≈ 0.
Model selection
Comparing the two models to select the one that best fit the study data, the Akaike Information Criteria and the Bayesian Information Criteria was used. The model that has the lowest AIC and the BIC is selected to be the best fit.
Likelihood function
Suppose a set of parameter value θ, with given x outcomes, then the likelihood function is the probability of those observed outcomes;
Suppose a given parameterized family of probability functions in the discrete distribution case;
where θ is the parameter, the likelihood function is
written
with x being the observed outcome of the data. Alternatively, when f(x | θ) is viewed as a function of x with fixed θ, it is a probability density function, and when viewed as a function of θ with x fixed, it is a likelihood function.
From a geometric standpoint, if we consider f (x, θ) as a function of two variables then the family of probability distributions can be viewed as a family of curves parallel to the x-axis, while the family of li
