Brand Awareness via Online Media: An Evidence Using Instagram Medium with Statistical Analysis

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.

Alpha Power Extended Inverse Weibull Poisson Distribution: Properties, Inference, and Applications to lifetime data

In this paper, a new four-parameter extended inverse Weibull distribution called Alpha power Extended Inverse Weibull Poisson distribution is introduced using the alpha power Poisson generator. This method adds two shape parameters to a baseline distribution thereby increasing its flexibility and applicability in modeling lifetime data. We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, and order statistics. We use the method of maximum likelihood technique for estimating the model parameters of Alpha power extended inverse Weibull distribution and the corresponding confidence intervals are obtained. The simulation method is carried out to evaluate the performance of the maximum likelihood estimate in terms of their Absolute Bias and Mean Square Error using simulated data. Two lifetime data sets are presented to demonstrate the applicability of the new model and it is found that the new model has superior modeling power when compare to Inverse Weibull distribution, Alpha Power Poisson inverse exponential distribution, Alpha Power Extended Inverse Weibull distribution, and Alpha Power Extended Inverse Exponential distribution.

Reliability estimation and parameter estimation for inverse Weibull distribution under different loss functions

In this paper, the classical and Bayesian estimators of the unknown parameters and the reliability function of the inverse Weibull distribution are considered. The maximum likelihood estimators (MLEs) and modified maximum likelihood estimators (MMLEs) are used in the classical parameter estimation. Bayesian estimators of the parameters are obtained by using symmetric and asymmetric loss functions under informative and non-informative priors. Bayesian computations are derived by using Lindley approximation and Markov chain Monte Carlo (MCMC) methods. The asymptotic confidence intervals are constructed based on the maximum likelihood estimators. The Bayesian credible intervals of the parameters are obtained by using the MCMC method. Furthermore, the performances of these estimation methods are compared concerning their biases and mean square errors through a simulation study. It is seen that the Bayes estimators perform better than the classical estimators. Finally, two real-life examples are given for illustrative purposes.

A generalization to the log-inverse Weibull distribution and its applications in cancer research

In this paper we consider a generalization of a log-transformed version of the inverse Weibull distribution. Several theoretical properties of the distribution are studied in detail including expressions for its probability density function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, percentile measures, entropy measures, median, mode etc. Certain structural properties of the distribution along with expressions for reliability measures as well as the distribution and moments of order statistics are obtained. Also we discuss the maximum likelihood estimation of the parameters of the proposed distribution and illustrate the usefulness of the model through real life examples. In addition, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated data sets.

Estimation of the Inverse Weibull Distribution Parameters under Type-I Hybrid Censoring

The hybrid censoring is a mixture of type-I and type-II censoring schemes. This paper presents the statistical inferences of the inverse Weibull distribution parameters when the data are type-I hybrid censored. First, we consider the maximum likelihood estimates of the unknown parameters. It is observed that the maximum likelihood estimates can not be obtained in closed form. We further obtain the Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. We also compute the approximate Bayes estimates using Lindley's approximation technique. The performance of the Bayes estimates have been compared with maximum likelihood estimates through the Monte Carlo Markov chain techniques. Finally, a real data set have been analysed for illustration purpose.

Different Classical Methods of Estimation and Chi-squared Goodness-of-fit Test for Unit Generalized Inverse Weibull Distribution

In this paper, we try to contribute to the distribution theory literature by incorporating a new bounded distribution, called the unit generalized inverse Weibull distribution (UGIWD) in the (0, 1) intervals by transformation method. The proposed distribution exhibits increasing and bathtub shaped hazard rate function. We derive some basic statistical properties of the new distribution. Based on complete sample, the model parameters are obtained by the methods of maximum likelihood, least square, weighted least square, percentile, maximum product of spacing and Cram`er-von-Mises and compared them using Monte Carlo simulation study. In addition, bootstrap confidence intervals of the parameters of the model based on aforementioned methods of estimation are also obtained. We illustrate the performance of the proposed distribution by means of one real data set and the data set shows that the new distribution is more appropriate as compared to unit Birnbaum-Saunders, unit gamma, unit Weibull, Kumaraswamy and unit Burr III distributions. Further, we construct chi-squared goodness-of-fit tests for the UGIWD using right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modification. The criterion test used is the modified chi-squared statistic Y^2, developedby Bagdonavi?ius and Nikulin, 2011 for some parametric models when data are censored. The performances of the proposed test are shown by an intensive simulation study and an application to real data set