The purpose of this paper is to investigate a new family of distributions based on an inverse trigonometric function known as the arctangent function. In the context of actuarial science, heavy-tailed probability distributions are immensely beneficial and play an important role in modelling data sets. Actuaries are committed to finding for such distributions in order to get an excellent fit to complex economic and actuarial data sets. The current research takes a look at a popular method for generating new distributions which are excellent candidates for dealing with heavy-tailed data. The proposed family of distributions is known as the Arctan-X family of distributions and is introduced using an inverse trigonometric function. For the specific purpose of the show of strength, we studied the Arctan-Weibull distribution as a special case of the developed family. To estimate the parameters of the Arctan-Weibull distribution, the frequentist approach, i.e., maximum likelihood estimation, is used. A rigorous Monte Carlo simulation analysis is used to determine the efficiency of the obtained estimators. The Arctan-Weibull model is demonstrated using a real-world insurance data set. The Arctan-Weibull is compared to well-known two-, three-, and four-parameter competitors. Among the competing distributions are Weibull, Kappa, Burr-XII, and beta-Weibull. For model comparison, we used the most precise tests used to know whether the Arctan-Weibull distribution is more useful than competing models.
Computer technology plays a prominent role in almost every aspect of daily life including education, health care, online shopping, advertising, and even in homes. Computers help to make daily tasks much easier and convenient. Among social media, YouTube is a well-known social sharing networking service. As more and more people join social media and become everyday users, brands have also increased their online engagement. However, it is still unclear how to effectively measure value and return on advertising using social media. As of 2021, more than 31 million YouTube channels around the globe have been opened. In this paper, we consider YouTube advertising to check its effectiveness and benefits gained. Certain statistical tools are adopted to measure the extent of advertising benefits and their correlation in creating effective advertising campaigns on YouTube. Simple linear regression analysis is performed on the data representing the YouTube advertising budget of a company and the sales data of that company. Furthermore, we develop a new statistical distribution to provide the best description of the YouTube advertising data. The result of this research shows that YouTube is an effective medium for advertising and has a strong relationship with sales.
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