Monsoon, post monsoon rainy days analysis by using normal, binomial distribution and discrete probability for south Gujarat

The analysis will be conducted for standard weekly (SW) 22 to 47 of monsoon and post monsoon season at south Gujarat. The standard weekly rainy days analysis of binomial distribution for monsoon season of Navsari on chi-square test on binomial distribution was found in standard week (SW) 22 to 31, 33 and standard week (SW) 35 to 39 and post monsoon in standard week (SW) 41 to 44 shows significant. The result also reveals that the monsoon season SW 32 and 34 and post monsoon season SW 40, 45, 46 and 47 revealed non-significant result. Analysis reveals the rainfall is not equally distributed during SW 32, 34, 40, 45, 16 and 47, so that the test of binomial distribution is a good fit. Monsoon season rainfall data of Navsari, Bharuch and Valsad reveals that the normal distribution at 10, 20 and 30% probability levels for the month of June, July, August and September shows the possibility of increasing rainy days occurrence. The Navsari and Bharuch districts during post monsoon season rainfall of months of October and November reveals decreasing tendency except Valsad district. The binomial distribution fit only those standard weeks in which rainfall is not equally distributed. The standard weekly rainy days analysis of binomial distribution on chi-square test in Bharuch was found that standard week (SW) 25 only 10% of monsoon season and in post monsoon standard week (SW) 42 and 47 shows non significant (5 and 10% level of significant) result, but SW 25 found significant at 5% level. In case of Valsad district, standard week 22 to 39 of monsoon season and in post monsoon season 41, 42, 43 and 46 standard weeks shows significant result. The result reveals that the monsoon season of Bharuch standard weeks 22 to 39 except from 25 and post monsoon 40, 41, 43, 44, 45 and 46 shows significant result. Further, in Valsad district standard weeks 40, 44, 45 and 47 shows significant result. The trend analysis of rainy days shows that increasing trend in monsoon season and decreasing trend in post monsoon season of Navsari, Bharuch and Valsad districts. From above results observed that the rainfall distribution is not equally distributed so test of binomial distribution at above given standard week is a good fit. The data also shows that, decreasing tendency in rainfall was observed except Valsad district.

Sustainability and authenticity: are they food risk relievers during the COVID-19 pandemic?

PurposeThe study jointly investigates sustainability and authenticity concepts in the food context during the COVID-19 outbreak with a fourfold objective: (1) understanding whether sustainability and authenticity are equivalent concepts in consumers' perceptions; (2) advancing knowledge on the role played by them about food frauds' perception; (3) investigating whether these concepts are considered as “risk relievers” by consumers, (4) comparing the concepts to understand which one has a greater weight on the consumer's perception.Design/methodology/approachThe study adopts a Combination of a Uniform and a shifted Binomial distribution (CUB models) on data gathered in Spain between June and August 2020 through an online questionnaire.FindingsThe findings reveal that: (1) consumers perceive sustainability and authenticity as different concepts in the food context and (2) as two important indicators of fraud protection of a product for consumers; (3) besides, authenticity is seen as a “risk reliever” in buying a food product, as well as sustainability, (4) although results underline high uncertainty in the latter case.Originality/valueBy considering that the COVID-19 outbreak seriously threatens food safety, security and nutrition, this research elucidates the relevant role of food sustainability and authenticity concepts as “risk relievers” in terms of food frauds and negative issues related to COVID-19.

GoPeaks: Histone Modification Peak Calling for CUT&Tag

Genome-wide mapping of the histone modification landscape is critical to understanding tran-scriptional regulation. Cleavage Under Targets and Tagmentation (CUT&Tag) is a new method for profiling the localization of covalent histone modifications, offering improved sensitivity and decreased cost compared with Chromatin Immunoprecipitation Sequencing (ChIP-seq). Here, we present GoPeaks, a peak calling method specifically designed for histone modification CUT&Tag data. GoPeaks implements a Binomial distribution and stringent read count cut-off to nominate candidate genomic regions. We compared the performance of GoPeaks against com-monly used peak calling algorithms to detect H3K4me3, H3K4me1, and H3K27Ac peaks from CUT&Tag data. These histone modifications display a range of peak profiles and are frequently used in epigenetic studies. We found GoPeaks robustly detects genome-wide histone modifica-tions and, notably, identifies H3K27Ac with improved sensitivity compared to other standard peak calling algorithms.

Exactly Computing the Tail of the Poisson-Binomial Distribution

We present ShiftConvolvePoibin, a fast exact method to compute the tail of a Poisson-binomial distribution (PBD). Our method employs an exponential shift to retain its accuracy when computing a tail probability, and in practice we find that it is immune to the significant relative errors that other methods, exact or approximate, can suffer from when computing very small tail probabilities of the PBD. The accompanying R package is also competitive with the fastest implementations for computing the entire PBD.

Influence of sequencing depth on the fidelity and sensitivity of 1%-5% low-frequency mutation detection and recommendation for standardization of sequencing depth

Sequencing depth has always played an important role in the accurate detection of low-frequency mutations. The increase of sequencing depth and the reasonable setting of threshold can maximize the probability of true positive mutation, or sensitivity. Here, we found that when the threshold was set as a fixed number of positive mutated reads, the probability of both true and false-positive mutations increased with depth. However, When the number of positive mutated reads increased in an equal proportion with depth (the threshold was transformed from a fixed number to a fixed percentage of mutated reads), the true positive probability still increased while false positive probability decreased. Through binomial distribution simulation and experimental test, it is found that the "fidelity" of detected-VAFs is the cause of this phenomenon. Firstly, we used the binomial distribution to construct a model that can easily calculate the relationship between sequencing depth and probability of true positive (or false positive), which can standardize the minimum sequencing depth for different low-frequency mutation detection. Then, the effect of sequencing depth on the fidelity of NA12878 with 3% mutation frequency and circulating tumor DNA (ctDNA of 1%, 3% and 5%) showed that the increase of sequencing depth reduced the fluctuation range of detected-VAFs around the expected VAFs, that is, the fidelity was improved. Finally, based on our experiment result, the consistency of single-nucleotide variants (SNVs) between paired FF and FFPE samples of mice increased with increasing depth, suggesting that increasing depth can improve the precision and sensitivity of low-frequency mutations.

Based on Knowledge Recognition and Using Binomial Distribution Function to Establish a Mathematical Model of Random Selection of Test Questions in the Test Bank

With the in-depth development of social reforms, the scientificization of enterprise online examinations has become more and more urgent and important. The key to realizing scientific examinations is the automation and rationalization of propositions. Therefore, the construction and realization of the test question bank is also more important. In the realization of the entire test question database, how to select satisfactory test questions randomly from a large number of test questions through the selection of test questions so that the average difficulty, discriminability, and reliability of the test are satisfactory? These requirements are also more important. Among them, random selection of questions is an important difficulty in the realization of the test question bank. In order to solve the difficulties of random selection of these test questions, the author combines the experience of constructing the test question bank and uses the discrete binomial distribution to draw conclusions. Random variables established the first mathematical model for topic selection. By determining the form of the test questions and the distribution of the difficulty of the test questions and then making it use a random function to select questions, this will achieve better results.

Four statistical models for wet-spell analysis

Wet-spell analysis is an important part of rainfall analysis. The distribution of the length of wet-spells provides useful information on the temporal distribution of rainfall. This distribution has traditionally been modelled through different probability distributions. Here we compare four such models, namely, Cochran's model, truncated Poisson distribution, truncated negative binomial distribution, and logarithmic series distribution. These comparisons are accomplished with help of application to five rainguage stations in India.

Negative Binomial Distribution to Explain the Domestic Fire Incidence in Nepal

Background: Fire disaster is one of the most destructive disasters. According to global dataset of Sendai Framework, domestic fire incidence was 9.9% up to 2019. In Nepal, 62% fire incidence was reported during 2017 and 2018. However, many studies have been conducted on fire incidence, few of them are based on domestic fire incidence. Objective: To find the descriptive statistics of fire occurrences and fire fatalities, and to identify the probability distributions that best fit the data of fire occurrences observed in three ecological regions as well as overall in Nepal. Material and Methods: The data of fire incidences from May 2011 to April 2021 were retrieved from Nepal Disaster Risk Reduction Portal, Government of Nepal. At first, a statistical software "Mathwave EasyFit" of 30 days trial version was used to identify the candidate probability models. Further, the best probability model was determined after testing the goodness of fit of the candidate models by using graphical tools-histogram and theoretical densities, empirical and theoretical CDFs, Q-Q plot and P-P plot; and mathematical tools-maximum likelihood, Akaike Information Criteria and Bayesian Information Criteria by using the package “fitdistrplus” of software R version 4.1.1. Results: On an average, 135 fire incidences per month were occurred in Nepal. However, the Terai faced the highest monthly fire incidences compared to the Hill and the Mountain, it has less fatality per 100 fire incidence followed by the Hill and the Mountain. Descriptive statistics reveals that fire occurrences are moderate during November to February and high in March and April. The fire incidences were reported high during spring and winter and low during summer and autumn season which reveals that fire incidence might be related with the precipitation and temperature. The sample data was run in "Mathwave EasyFit" software which suggested Poisson, geometric and negative binomial distribution as candidate probability models. The goodness of fit of these models were further tested by graphical as well as mathematical tools where negative binomial distribution was found to be best among the candidate models for the data set. Conclusion: Incidence of fire disasters varies by ecological regions as well as by seasons. It is low in the Mountain region and during Monsoon/rainy season. Negative binomial distribution fits the best to monthly data of fire incidence in Nepal.

A New Neutrosophic Negative Binomial Distribution: Properties and Applications

Many problems in real life exist that are full of confusion, vagueness, and ambiguity. The quantification of such issues in a scientific way is the need of time. The negative binomial distribution is an important discrete probability distribution from the account of classical probability distribution theory. The distribution was used to study the chance of kth success in n trials before n − 1 failures for crisp data. The literature lacks in dealing with the situations for interval-valued data under negative binomial distribution. In this research, the neutrosophic negative binomial distribution is proposed to generalize the classical negative binomial distribution. The generalized proposed distribution considers the indeterminacy and crisp form from interval-valued. Several properties of the proposed distribution, such as moment generating function, characteristic function, and probability generating function, are also derived. Furthermore, the derivation of reliability analysis properties such as survival, hazard rate, reversed hazard rate, cumulative hazard rate, mills ratio, and odds ratio are also presented. In addition, order statistics for the proposed distribution, including w th , joint, median, minimum, and maximum order statistics are part of the paper. The proposed distribution is discussed from the real data applications perspective by considering the different case studies. This research opens the way to deal with the problems that follow conventional conveyances and include nonprecisely determined details simultaneously.