Let j be a holomorphic self-map and g a fixed holomorphic function on the unit ball B. The boundedness and compactness of the Volterra composition operatorTg, j ¦ (z)=ò10 ¦ (j (tz) Rg(tz) dt/ton the logarithmic Bloch space and little logarithmic Bloch space are studied in this paper.

In this paper, we introduce a new five-parameter distribution with increas-ing, decreasing, bathtub-shaped failure rate called the Beta-Weibull-Logarithmic (BWL) distribution. Using the Sterling Polynomials, various properties of the new distribu-tion such as its probability density function, its reliability and failure rate functions, quantiles and moments, Renyi and Shannon entropies, moments of order statistics, Bonferroni and Lorenz curves were derived. then the maximum likelihood estimation of BWL distribution for the parameters of BWL distribution are found. Finally the usefulness of this distribution for real data are presented.

In survival data modeling, the numbers of components of composite distributions in failure times play an essential role, and in parallel, determining the appropriate distribution for the number of components increases the efficiency of estimators. In recent years, many distributions have been proposed by researchers to determine the number of components, such as binomial, geometric, Poisson and truncated Poisson distributions. Considering the importance of the subject, in this article, considering the logarithmic series distribution for the number of components in the compound inverse Weibull distribution, the inverse Weibull logarithmic series distribution is introduced. In the following, while estimating its parameters in different ways using simulation, the estimators are compared using the mean square error criterion. At the end, using the real data, the fit of the inverse Weibull logarithmic series distribution is checked.