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.
Marketing refers to the strategies a company undertakes to promote its brands to its potential audience. Advertising provides useful venues for marketing to promote a company’s survives/goods to the audience. It has a positive impact on the sale of services or products. In this study, we consider a well-known online medium called Twitter (the fourth most popular social media platform used by marketers) to check its impact on sales. For this purpose, the simple linear regression modeling approach is implemented to test the significance and usefulness of Twitter advertising on sale. Statistical tests such as t-test and correlation test are adopted to test the hypothesis of the “impact of Twitter advertising on sales.” Based on the findings of this study, it is observed that Twitter advertising has a positive impact on sales. Furthermore, a new statistical model called the exponential T-X exponentiated exponential is introduced. The proposed model is very interesting and possesses heavy-tailed characteristics which are useful in finance and other related sectors. Finally, the applicability of the new model is illustrated by considering the sales data.
Online marketing refers to the practices of promoting a company’s brand to its potential customers. It helps the companies to find new venues and trade worldwide. Numerous online media such as Facebook, YouTube, Twitter, and Instagram are available for marketing to promote and sell a company’s product. However, in this study, we use Instagram as a marketing medium to see its impact on sales. To carry out the computational process, the approach of linear regression modeling is adopted. Certain statistical tests are implemented to check the significance of Instagram as a marketing tool. Furthermore, a new statistical model, namely a new generalized inverse Weibull distribution, is introduced. This model is obtained using the inverse Weibull model with the new generalized family approach. Certain mathematical properties of the new generalized inverse Weibull model such as moments, order statistics, and incomplete moments are derived. A complete mathematical treatment of the heavy-tailed characteristics of the new generalized inverse Weibull distribution is also provided. Different estimation methods are discussed to obtain the estimators of the new model. Finally, the applicability of the new generalized inverse Weibull model is established via analyzing Instagram advertising data. The comparison of the new distribution is made with two other models. Based on seven analytical tools, it is observed that the new distribution is a better model to deal with data in the business, finance, and management sectors.
A long testing period is usually required for the life testing of high-reliability products or materials. It is possible to shorten the testing process by using ALTs (accelerated life tests). Due to the fact that ALTs test products in harsher settings than are typical use conditions, the life expectancy of the objects they evaluate is reduced. Censored data in which the specific failure timings of all units assigned to test are not known, or all units assigned to test have not failed, may arise in ALTs for a variety of reasons, including operational failure, device malfunction, expense, and time restrictions. In this paper, we have considered the step stress partially accelerated life test (SSPALT) under two different censoring schemes, namely the type-I progressive hybrid censoring scheme (type-I PHCS) and the type-II progressive censorship scheme (type-II PCS). The failure times of the items are assumed to follow NH distribution, while the tampered random variable (TRV) model is used to explain the effect of stress change. In order to obtain the estimates of the unknown parameters, the maximum likelihood estimation (MLE) approach is adopted. Furthermore, based on the asymptotic theory of MLEs, the approximate confidence intervals (ACIs) are also constructed. The point estimates under two censoring schemes are compared in terms of root mean squared errors (RMSEs) and relative absolute biases (RABs), while ACIs are compared in terms of their lengths and coverage probabilities (CPs). The performance of the estimators has been evaluated and compared under two censoring schemes with various sample sizes through a simulation study. Simulation results show that estimates with type-I PHCS outperform estimates with type-II PCS in terms of RMSEs, RABs, lengths, and CPs. Finally, a real-world numerical example of insulating fluid failure times is presented to show how the approaches will work in reality.
Introduction Rhinoplasty, a cosmetic surgical procedure aimed at altering the appearance of the nose, has gained immense popularity worldwide. Patients undergo this procedure for various reasons, ranging from aesthetic concerns to functional impairments. Social media, being a ubiquitous platform for sharing and consuming visual content, has emerged as a potential influencer for individuals contemplating rhinoplasty. This study aims to investigate the impact of social media on the prevalence of rhinoplasty among individuals residing in the southern and western regions of Saudi Arabia. Methods A cross-sectional study was conducted through an online self-administered questionnaire, targeting male and female adults aged 18 years or older, residing in the western and southern regions of Saudi Arabia. The questionnaire comprised 17 questions, categorized into two sections. The first section sought demographic information, including age, gender, education, and other relevant characteristics. The second section focused on the influence of social media on the decision-making process related to rhinoplasty. Results A total of 1645 participants responded to the survey, with 96.80% being Saudi citizens. The majority of respondents were females (69.11%); 58.52% of the respondents were from the western region of Saudi Arabia, while 41.48% lived in the southern region. Most participants (64.27%) were aged between 18 and 30 years. The study revealed that Snapchat (Snap Inc., Santa Monica, California, United States) was the most influential social media platform, with 43.41% of respondents reporting it as the key influencer for their decision to undergo rhinoplasty. Twitter (Twitter, Inc., San Francisco, California, United States) and Instagram (Meta Platforms, Inc., Menlo Park, California, United States) followed at 22.97% and 12.09%, respectively. Interestingly, 28.42% of respondents acknowledged that social media played a significant role in their decision to undergo rhinoplasty, particularly when promoted by celebrities or trusted figures. Comparing responses from the western and southern regions, the study showed that individuals from the southern region were relatively more influenced by social media, with 27.8% and 29.3% of respondents reporting the influence from the two regions, respectively. Out of the total respondents, only 38.75% reported dissatisfaction with their nose's appearance and condition, while 23.60% expressed a tendency towards undergoing rhinoplasty. Conclusion The study's findings underscore the critical role of social media in influencing patients' decisions to undergo rhinoplasty, particularly in the southern region of Saudi Arabia. Snapchat emerged as the most influential social media platform, with celebrities' pictures before and after the procedure being the leading factor in motivating patients to undergo rhinoplasty. The study highlights the need for further research to explore the potential risks and benefits asso...
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