Note: Correction to "Maximum Likelihood Estimation in the Birth-and-Death Process"

Maximum Likelihood Estimation in the Birth-and-death Process By

Step change point estimation in the multivariate-attribute process variability using artificial neural networks and maximum likelihood estimation

In some statistical process control applications, the combination of both variable and attribute quality characteristics which are correlated represents the quality of the product or the process. In such processes, identification the time of manifesting the out-of-control states can help the quality engineers to eliminate the assignable causes through proper corrective actions. In this paper, f...

Note: Maximum Likelihood Estimation for Markov Chains

1 Derivation of the MLE for Markov chains To recap, the basic case we’re considering is that of a Markov chain X∞ 1 with m states. The transition matrix, p, is unknown, and we impose no restrictions on it, but rather want to estimate it from data. The parameters we wish to infer are thus them matrix entries pij , which are defined as pij = Pr (Xt+1 = j|Xt = i) (1) What we observe is a sample fr...

Note: Maximum Likelihood Estimation for Markov Chains

1 Derivation of the MLE for Markov chains To recap, the basic case we’re considering is that of a Markov chain X∞ 1 with m states. The transition matrix, p, is unknown, and we impose no restrictions on it, but rather want to estimate it from data. The parameters we wish to infer are thus them matrix entries pij , which are defined as pij = Pr (Xt+1 = j|Xt = i) (1) What we observe is a sample fr...

Maximum Likelihood Estimation of Parameters in Generalized Functional Linear Model

Sometimes, in practice, data are a function of another variable, which is called functional data. If the scalar response variable is categorical or discrete, and the covariates are functional, then a generalized functional linear model is used to analyze this type of data. In this paper, a truncated generalized functional linear model is studied and a maximum likelihood approach is used to esti...