PRELIMINARY DESIGN OF ANALOG DISCRETE UNIFORM NOISE GENERATOR

The paper presents the basic idea of ​​the construction of an analog discrete uniform noise generator. The source of noise is a carbon resistor, the noise is linearly strongly amplified and limited to around zero. The probability density function (PDF) of the carbon resistor thermal noise in that region is square. By narrowing the symmetric allowable gap (interval) around zero, PDF of the noise approaches a uniform distribution. The factor of deviation from the uniform distribution is correctly and precisely defined. This quantity has been shown to be practically negligible. In addition, the paper discusses the application of the proposed ditheter noise, both in the two-bit and in the multi-bit stochastic digital measurement method (SDMM). It has been shown that noise is more suitable for application in multi-bit SDMM, because it is less sensitive to deviations from the uniform distribution. Commercially available track-and-hold circuits provide at least an order of magnitude wider bandwidth of the described generator compared to the standard solution that uses numerical random number generator and a corresponding D/A converter. However, the realization of such a generator requires hard engineering work, and therefore goes beyond the scope of this paper.

Statistical Distribution of Lassa Fever in Edo State, Nigeria

Lassa fever is a severe viral infection caused by the Lassa virus and spread by contact with excretions or secretions of infected rats gaining access to food and water inside human houses and other human activity areas. Sierra Leone, the Republic of Guinea, Nigeria, and Liberia are among the nations where it is endemic with a high number of deaths recorded yearly due to Lassa fever. In Nigeria, one of the states with the highest incidence is Edo. In order to reduce and predict the spread of Lassa fever in Edo state, the trend of the disease needs to be understood. Knowledge of the statistical distribution of a disease is one of the best ways to understand the trend of the disease. Currently, existing research on the statistical distribution of Lassa fever is very rare. The present work is an attempt to initiate research on the statistical distribution of Lassa fever with data obtained on weekly cases of Lassa Fever in Edo State, Nigeria. Based on the Kolmogorov Smirnoff and Anderson Darling’s goodness of fit test for fitting distribution, the Geometric distribution outfitted the weekly confirmed incidences of Lassa fever in Edo State, Nigeria when compared with the Discrete Uniform and Poisson distributions. The study further revealed that on the average, two Lassa fever cases is recorded per week in Edo State within the study period. This number of cases per week is on the high side and should be immediately looked into.

Characterizations of the Exponentiated Marshall-Olkin Discrete Uniform Distribution

In this short paper, we consider certain characterizations of the Exponentiated Marshall-Olkin Discrete Uniform (EMODU) distribution introduced by Gharib et al. (2017) to complete in some manner, the authors'  work

Expectation Identity of the Discrete Uniform Distribution and Its Application in the Calculations of Higher-Order Origin Moments

We provide a novel method to analytically calculate the high-order origin moments of a Discrete Uniform (DU) random variable, that is, the expectation identity method. First, the expectation identity of the DU distribution is discovered and summarized in a theorem. After that, we analytically calculate the first four origin moments and the general kth (k=1,2,…) origin moment of the DU distribution by the expectation identity method. After comparing the corresponding coefficients on both sides of an equation, we obtain a nonhomogeneous linear equations of first degree in k+1 variables. Furthermore, we have provided two ways to solve the nonhomogeneous linear equations. The first way is by matrix inversion, and the second way is by iterative solving. Moreover, the coefficients of the first ten origin moments of the DU distribution are summarized in a table. Finally, we have a proposition for special summations.

Discrete uniform and binomial distributions with infinite support

We study properties of two probability distributions defined on the infinite set $$\{0,1,2, \ldots \}$$ { 0 , 1 , 2 , … } and generalizing the ordinary discrete uniform and binomial distributions. Both extensions use the grossone-model of infinity. The first of the two distributions we study is uniform and assigns masses $$1/\textcircled {1}$$ 1 / 1 to all points in the set $$ \{0,1,\ldots ,\textcircled {1}-1\}$$ { 0 , 1 , … , 1 - 1 } , where $$\textcircled {1}$$ 1 denotes the grossone. For this distribution, we study the problem of decomposing a random variable $$\xi $$ ξ with this distribution as a sum $$\xi {\mathop {=}\limits ^\mathrm{d}} \xi _1 + \cdots + \xi _m$$ ξ = d ξ 1 + ⋯ + ξ m , where $$\xi _1 , \ldots , \xi _m$$ ξ 1 , … , ξ m are independent non-degenerate random variables. Then, we develop an approximation for the probability mass function of the binomial distribution Bin$$(\textcircled {1},p)$$ ( 1 , p ) with $$p=c/\textcircled {1}^{\alpha }$$ p = c / 1 α with $$1/2<\alpha \le 1$$ 1 / 2 < α ≤ 1 . The accuracy of this approximation is assessed using a numerical study.

Generalized Lichen Nitidus in a Middle-Aged Adult

Lichen nitidus (LN) is a benign micropapular eruption of unknown etiology that often follows an unpredictable course. LN typically affects children and young adults and presents with asymptomatic, discrete, uniform, skin colored, pin-point sized papules.1 These papules are commonly found on the chest, abdomen, flexor surfaces of the upper extremities, dorsal hand, and anogenital region.1 Focal presentation is more common while generalized distribution of LN is rarer and seen more exclusively in pediatric patients.2 Although patients are typically asymptomatic, pruritus is sometimes a noted symptom.1 We report the diagnosis and treatment of an uncommon case of generalized LN in a middle-aged adult.

SUPERPOSITIONED STATIONARY COUNT TIME SERIES

This paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.