Solution. Since the logarithm is strictly monotonically increasing, the maximiser of the log-likelihood equals the maximiser of the likelihood. It is easier to take derivatives for the log-likelihood function than for the likelihood function so that the maximum likelihood estimate is typically determined using the log-likelihood. Given the algebraic expression of `(θ), it is simpler to work wit...

This paper measures the mean, standard deviation, alpha, and beta of venture capital investments, using a maximum likelihood estimate that corrects for selection bias. The biascorrected estimation neatly accounts for log returns. It reduces the estimate of the mean log return from 108% to 15%, and of the log market model intercept from 92% to 7%: The selection bias correction also dramatically ...

A quantitative structure-property relationship (QSPR) model is developed to predict the logarithm of the soil sorption coefficient of 82 organic compounds. The data set contains polar and nonpolar, saturated, unsaturated, aliphatic, aromatic, and polycyclic aromatic compounds covering a log K(oc) range from about 1 to 6 log units. The best correlation equation, containing only five constitution...

For a family of bond percolation models on Z that includes the FortuinKasteleyn random cluster model, we consider properties of the “droplet” that results, in the percolating regime, from conditioning on the existence of an open dual circuit surrounding the origin and enclosing at least (or exactly) a given large area A. This droplet is a close surrogate for the one obtained by Dobrushin, Kotec...

Logs contain valuable information about the runtime behaviors of software systems. Thus, practitioners rely on logs for various tasks such as debugging, system comprehension, and anomaly detection. However, are difficult to analyze due their unstructured nature large size. In this paper, we propose a novel approach called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http:...

It is contentious whether size variation among mammalian teeth is heterogeneous or homogeneous, whether the coefficient of variation is reliable, and whether the standard deviation of log-transformed data and the residual of standard deviation on mean variable size are useful replacements for the coefficient of variation. Most studies of tooth size variation have been on mammals with complex-cr...