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In today's modern world, marketing is a fruitful source to grow a business by reaching a larger audience. This paper considers a popular social media source called LinkedIn.com as a way of marketing or reaching a larger audience. We consider a regression approach to explore the statistically significant role of the LinkedIn medium as a tool for reaching a larger audience. In addition to statistically exploring the role of the LinkedIn medium in the financial sector, we also introduce a new Weibull-based probability distribution, namely, the exponential TX inverse Weibull (for short'ETXI-Weibull') distribution. The ETXI-Weibull distribution is specially designed for analyzing LinkedIn marketing data. The beauty of the ETXI-Weibull distribution is that it satisfies the heavy-tailed characteristics, which are explored visually and mathematically. For the ETXI-Weibull distribution, the estimators are derived whose performances are evaluated visually and numerically through a simulation study. The ETXI-Weibull distribution is applied practically by considering the LinkedIn marketing data set as an example. Using certain established statistical tests, we observe that the ETXI-Weibull distribution provides an optimal fit to the LinkedIn marketing data set. Furthermore, a bivariate extension of the exponential TX inverse Weibull model is also introduced. Finally, the bivariate extension of the exponential TX inverse Weibull model is illustrated by modeling the LinkedIn marketing and sales data.