[6] **viXra:1712.0504 [pdf]**
*submitted on 2017-12-18 15:14:48*

**Authors:** Samir Ait-Amrane

**Comments:** 12 Pages. In French

In this paper, we will explain some basic notions of statistics, first in the case of one variable, then in the case of two variables, while organizing ideas and drawing a parallel between some statistical and probabilistic formulas that are alike. We will also say a brief word about econometrics, time series and stochastic processes and provide some bibliographical references where these notions are explained clearly.

**Category:** Statistics

[5] **viXra:1712.0499 [pdf]**
*submitted on 2017-12-18 06:33:01*

**Authors:** Jason Lind

**Comments:** 2 Pages.

Development a novel closed form, for integer bounds, of Truncated Distribution and an application of that to a weighting function that favors values further from the origin.

**Category:** Statistics

[4] **viXra:1712.0429 [pdf]**
*submitted on 2017-12-14 01:05:01*

**Authors:** Cres Huang

**Comments:** Pages.

Viewing the random motions of objects, an observer might think it is 50-50 chances that an object would move toward or away. It might be intuitive, however, it is far from the truth. This study derives the probability functions of Doppler blueshift and redshift effect of signal detection.
The fact is, Doppler redshift detection is highly dominating in space, surface, and linear observation. Under the conditions of no quality loss of radiation over distance, and the observer has perfect vision; It is more than 92% probability of detecting redshift, in three-dimensional observation, 87% surface, and 75\% linear. In cosmic observation, only 7.81% of the observers in the universe will detect blueshift of radiations from any object, on average. The remaining 92.19% of the observers in the universe will detect redshift. It it universal for all observers, aliens or Earthlings at all locations of the universe.

**Category:** Statistics

[3] **viXra:1712.0244 [pdf]**
*replaced on 2018-01-13 13:47:16*

**Authors:** Luca Martino

**Comments:** 46 Pages. (to appear) Digital Signal Processing, 2018.

Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of a-posteriori estimators which are often expressed as complicated multi-dimensional integrals. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and Monte Carlo methods are the only feasible approach. A very powerful class of Monte Carlo techniques is formed by the Markov Chain Monte Carlo (MCMC) algorithms. They generate a Markov chain such that its stationary distribution coincides with the target posterior density. In this work, we perform a thorough review of MCMC methods using multiple candidates in order to select the next state of the chain, at each iteration. With respect to the classical Metropolis-Hastings method, the use of multiple try techniques foster the exploration of the sample space. We present different Multiple Try Metropolis schemes, Ensemble MCMC methods, Particle Metropolis-Hastings algorithms and the Delayed Rejection Metropolis technique. We highlight limitations, benefits, connections and dierences among the different methods, and compare them by numerical simulations.

**Category:** Statistics

[2] **viXra:1712.0110 [pdf]**
*submitted on 2017-12-04 22:02:28*

**Authors:** D Williams

**Comments:** 8 Pages.

A possible alternative (and non-standard) model of probability is presented based on non-standard "dx-less" integrals. The possibility of other such models is discussed.

**Category:** Statistics

[1] **viXra:1712.0018 [pdf]**
*submitted on 2017-12-03 02:40:26*

**Authors:** Ilija Barukčić

**Comments:** 50 pages. Copyright © 2017 by Ilija Barukčić, Horandstrasse, Jever, Germany. Published by:

Objective: Many times a positive relationship between Helicobacter pylori infection and gastric cancer has been reported, yet findings are inconsistent.
Methods: A literature search in PubMed was performed to re-evaluate the relationship between Helicobacter pylori (HP) and carcinoma of human stomach. Case control studies with a least 500 participants were consider for a review and meta-analysis. The meta-/re-analysis was conducted using conditio-sine qua non relationship and the causal relationship k. Significance was indicated by a p-value of less than 0.05.
Result: All studies analyzed provide impressive evidence of a cause effect relationship between H. pylori and gastric cancer (GC). Two very great studies were able to make the proof that H. pylori is a necessary condition of human gastric cancer. In other words, without H. pylori infection no human gastric cancer.
Conclusion: Our findings indicate that Helicobacter pylori (H. pylori) is the cause of gastric carcinoma.

**Category:** Statistics