Let$ P_{n}(x)= sum_{i=0}^{n} A_{i}x^{i}$ be a random algebraicpolynomial, where $A_{0},A_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. Thus $A_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}H_{j}(t)}$, where $H_j(t)$'s are complex slowlyvarying functions.Under the assumption that there exist ...

We give FPT-hardness for setcover and clique with super exponential time in the parameter k. Under the ð and pgc we prove that setcover admits no log k ratio, for c > 0 for any algorithm with running t(k) = exp ( k(log k) f ) ) · poly(n) for constant f > 0. Under the eth alone, we prove that setcover admits no √ log k ratio, in time exp ( k(log f k) ) · poly(n) for constant f > 0. Under the eth...

We use a two-parameter family of bounded distribution functions (Kumaraswamy) to fit electronic textbook (etext) usage in 20 blended and online courses from Michigan State University, MIT, and edX. We observe clusters of courses in the parameter space that correlate with course structural features such as frequency of exams.

Data from a 2-parameter Weibull distribution (with covariates) is traditionally analyzed on a logarithmic scale to take advantage of the resulting location-scale nature of the transformed data Y1, . . . , Yn. Quantities of interest are the regression parameters β, the scale parameter σ, the p-quantile yp(u) = u′β+σ log(− log(1− p)), the tail probability p(y|u) = P (Y ≤ y|u) = 1−exp(− exp((y−u′β...

We consider the AR(1) time series model Xt − βXt−1 = ξt, β−p ∈ N {1}, when Xt has Beta distribution B(p, q), p ∈ (0, 1], q > 1. Special attention is given to the case p = 1 when the marginal distribution is approximated by the power law distribution closely connected with the Kumaraswamy distribution Kum(p, q), p ∈ (0, 1], q > 1. Using the Laplace transform technique, we prove that for p = 1 th...

Finding new families of distributions has become a popular tool in statistical research. In this article, we introduce a new flexible four-parameter discrete model based on the Marshall-Olkin approach, namely, the discrete Kumaraswamy Marshall-Olkin exponential distribution. The proposed distribution can be viewed as another generalization of the geometric distribution and enfolds some importan...

Here we report the experimental log maximum fluxes of n = 9 non-steroidal anti-inflammatory drugs (NSAID) through silicone membranes from the lipid mineral oil (experimental (Exp.) log JMPMO) and correlate those Exp. log JMPMO values with their experimental log maximum fluxes through human skin in vivo from mineral oil (Exp. log JMHMO). The correlation was only fair (r2 = 0.647) for n = 9 but i...