In this paper, a new modified Kumaraswamy distribution is proposed, and some of its basic properties are presented, such as the mathematical expressions for moments, probability weighted order statistics, quantile function, reliability, entropy measures. The parameter estimation done via maximum likelihood method. to show usefulness proposed model, well-established actuarial measures value-at-r...

The Kumaraswamy distribution is an important probability used to model several hydrological problems as well various natural phenomena whose process values are bounded on both sides. In this paper, we introduce a new family of inverse and then explore its statistical properties. Conventional maximum likelihood estimators considered for the parameters estimation based dual generalized order stat...

There are a few particular functions whose properties under rational approximation have received special scrutiny. Exp and log are probably the central examples. This stems both from the fact that we can actually work out the details, though by no means trivially (see, for example, [9] or [11]) and from the pivotal role of these functions in applied analysis. It is also the case that almost all...

By conventional wisdom, a feature that occurs too often or too rarely in a genome can indicate a functional element. To infer functionality from frequency, it is crucial to precisely characterize occurrences in randomly evolving DNA. We find that the frequency of oligonucleotides in a genomic sequence follows primarily a Pareto-lognormal distribution, which encapsulates lognormal and power-law ...

The derivation of the noise covariance of the ith projection view in Equation (5) is similar to the Appendix of Tilley et al. [22]; the difference is that our application is for DBT geometry in which the imaged volume is very close to the detector. As a result, we neglect the focal spot blur so the blurring operation in our study only includes the detector blur. For the directly measured projec...

We analyze the temporal structure of long (T90 > 2sec) and short (T90 < 2sec) BATSE bursts. We find that: (i) In many short bursts δtmin/T ≪ 1 (where δtmin is the shortest pulse). This indicates that short bursts arise, like long ones, in internal shocks. (ii) In long bursts there is an excess of long intervals between pulses (relative to a lognormal distribution). This excess can be explained ...

The first laboratory confirmation of stochastic growth theory is reported. Floating potential fluctuations are measured in a vacuum arc centrifuge using a Langmuir probe. Statistical analysis of the energy density reveals a lognormal distribution over roughly 2 orders of magnitude, with a high-field nonlinear cutoff whose spatial dependence is consistent with the predicted eigenmode profile. Th...

Given $\beta\in(0,1)$, we show the existence of a Beurling generalized number system whose integer counting satisfies $N(x) = ax + O\bigl(x\exp(-c\log^{\beta} x)\bigr)$ for some $a>0$ and $c>0$, prime function $\pi(x) \mathrm{Li}(x) \Omega\bigl(x\exp(-c'(\log x)^{\frac{\beta}{\beta+1}})\bigr)$ $c'>0$. This is done by generalizing construction Diamond, Montgomery, Vorhauer. serves as additional ...

Due to the advance computer technology, use of probability distributions has been raised up solve real life problems. These applications are found in reliability engineering, sciences, economics, psychology, survival analysis, and some others. This study offers a new model called Marshall–Olkin Extended Gumbel Type-II (MOEGT-II) which can various shapes failure rate function. The proposed distr...

We present the best known separation between tree-like and general resolution, improving on the recent exp(n) separation of BEGJ98]. This is done by constructing a natural family of contradictions, of size n, that have O(n)-size resolution refutations, but only exp(((n= log n))-size tree-like refutations. This result implies that the most commonly used automated theorem procedures, which produc...