Measure of dispersion is an important statistical tool used to illustrate the distribution of datasets.The use of this measure has allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers have been able to develop measures of dispersion from the mean such as mean deviation, mean absolute deviation, variance and standard deviation. Studies have shown that standard deviation is currently the most efficient measure of variation about the mean and the most popularly used measure of variation about the mean around the world because of its fewer shortcomings. However, studies have also established that standard deviation is not 100% efficient because the measure is affected by outlier in thedatasets and it also assumes symmetry of datasets when estimating the average deviation about the mean a factor that makes it to be responsive to skewed datasets hence giving results which are biased for such datasets. The aim of this study is to make a comparative analysis of the precision of the geometric measure of variation and standard deviation in estimating the average variationabout the mean for various datasets. The study used paired t-test to test the difference in estimates given by the two measures and four measures of efficiency (coefficient of variation, relative efficiency, mean squared error and bias) to assess the efficiency of the measure. The results determined that the estimates of geometric measure were significantly smaller than those of standard deviation and that the geometric measure was more efficient in estimating the average deviation for geometric, skewed and peaked datasets. In conclusion, the geometric measure was not affected by outliers and skewed datasets, hence it was more precise than standard deviation.

Organizations and companies are starving to improve their business processes to stay in competition. As we know that process mining is a young and emerging study that lasts among data mining and machine learning. The main goal of process mining is to obtain accurate information from the data; therefore, in recent years, it attracts the attention of many researchers, practitioners, and vendors. However, the purpose of enhancement is to extend or develop an existing process model by taking information from the actual process recorded in an event log. One type of enhancement of a process mining model is repair. It is common practice that due to logging errors in information systems or the presence of a special behavior process, they have the actual event logs with the noise. Hence, the event logs are traditionally thought to be defined as situation. Actually, when the logging is based on manual logging i.e., entering data in hospitals when patients are admitted for treatment while recording manually, events and timestamps are missing or recorded incorrectly. Our paper is based on theoretical and practical research work. The main purpose of our study is to use the knowledge gather from the process model, and give a technique to repair the missing events in a log. However, this technique gives us the analysis of incomplete logs. Our work is based on time and data perspectives. As our proposed approach allows us to repair the event log by using stochastic Petri net, alignment, and converting them into Bayesian analysis, which improves the performance of the process mining model. In the end, we evaluate our results by using the algorithms described in the alignment and generate synthetic/artificial data that are applied as a plug-in in a process mining framework ProM.

Surprising perceptions may happen in survey sampling. The arithmetic mean estimator is touchy to extremely enormous or potentially small observations, whenever selected in a sample. It can give one-sided (biased) results and eventually, enticed to erase from the selected sample. These extremely enormous or potentially small observations, whenever known, can be held in the sample and utilized as supplementary information to expand the exactness of estimates. Also, a supplementary variable is consistently a well-spring of progress in the exactness of estimates. A suitable conversion/transformation can be utilized for getting much more precise estimates. In the current study, regarding population mean, we proposed a robust class of separate type quantile regression estimators under stratified random sampling design. The proposed class is based on extremely enormous or potentially small observations and robust regression tools, under the framework of Särndal. The class is at first defined for the situation when the nature of the study variable is nonsensitive, implying that it bargains with subjects that do not create humiliation when respondents are straightforwardly interrogated regarding them. Further, the class is stretched out to the situation when the study variable has a sensitive nature or theme. Sensitive and stigmatizing themes are hard to explore by utilizing standard information assortment procedures since respondents are commonly hesitant to discharge data concerning their own circle. The issues of a population related to these themes (for example homeless and nonregular workers, heavy drinkers, assault and rape unfortunate casualties, and drug users) contain estimation errors ascribable to nonresponses as well as untruthful revealing. These issues might be diminished by upgrading respondent participation by scrambled response devices/techniques that cover the genuine value of the sensitive variable. Thus, three techniques (namely additive, mixed, and Bar-Lev) are incorporated for the purposes of the article. The productivity of the proposed class is also assessed in light of real-life dataset. Lastly, a simulation study is also done to determine the performance of estimators.

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Measures of dispersion are important statistical tool used to illustrate the distribution of datasets. These measureshave allowed researchers to define the distribution of various datasets especially the measures of dispersion from the mean. Researchers and mathematicians have been able to develop measures of dispersion from the mean such as mean deviation, variance and standard deviation. However, these measures have been determined not to be perfect, for example, variance giveaverage of squared deviation which differ in unit of measurement as the initial dataset, mean deviation gives bigger average deviation than the actual average deviation because it violates the algebraic laws governing absolute numbers, while standard deviation is affected by outliers and skewed datasets. As a result, there was a need to develop a more efficient measure of variation from the mean that would overcome these weaknesses. The aim of the paper was to estimate the average variation about the population mean using geometric measure of variation. The study was able to use the geometric measure of variation to estimate the average variation about the population mean for un-weighted datasets, weighted datasets, probability mass and probability density functions with finite intervals, however, the function faces serious integration problems when estimating the average deviation for probability density functions as a result of complexity in the integrations by parts involved and alsointegration on infinite intervals. Despite the challenge on probability density functions, the study was able to establish that the geometric measure of variation was able to overcome the challenges faced by the existing measures of variation about the population mean.