On the Flexibility of Topp Leone Exponentiated Inverse Exponential Distribution

Abstract

In this paper, we introduced a new continuous probability distribution called the Topp Leone exponentiated inverse exponential distribution with three parameters. We studied the nature of proposed distribution with the help of its mathematical and statistical properties such as quantile function, ordinary moments, moment generating function, survival function and hazard function. The probability density function of order statistic for this distribution was also obtained. We performed classical estimation of parameters by using the technique of maximum likelihood estimate. The proposed model was applied to two reallife datasets. The first data set has to do with patients with cancer of tongue with aneuploidy DNA profile and the second data set has to do with patients who were diagnosed with hypertension and received at least one treatment related to hypertension. The results showed that the new distribution provided better fit than other distributions presented. As such, it can be categorically said that the Topp Leone exponentiated inverse exponential distribution is good distribution in modeling survival data.

Kumaraswamy-Odd Rayleigh-G Family of Distributions with Applications

“…Data set III represents 101 data points that reflect the stress-rupture life of kevlar 49/epoxy strands which were subjected to continuous persistent pressure at the 90 percent stress point until everything had collapsed as in [20]. Data set IV represents the death times (in weeks) of patients with cancer of tongue with aneuploidy DNA profile as reported by [21]. Data set V is due to [21] which is a life times data relating to times (in months from 1 st January, 2013 to 31 st July, 2018) of 105 patients who were diagnosed with hypertension and received at least one treatment related to hypertension in the hospital where death is the event of interest.…”

“…Data set IV represents the death times (in weeks) of patients with cancer of tongue with aneuploidy DNA profile as reported by [21]. Data set V is due to [21] which is a life times data relating to times (in months from 1 st January, 2013 to 31 st July, 2018) of 105 patients who were diagnosed with hypertension and received at least one treatment related to hypertension in the hospital where death is the event of interest.…”

“…(a) For known parameter values i.e. quantile function defined in Equation(21). (b) Using the maximum likelihood method, we compute the MLE of ˆi α , ˆi τ , ˆi λ , and ˆi δ for the i th replicate.…”

The Topp-Leone Generalized Inverted Exponential Distribution with Real Data Applications

“…Furthermore, there were many authors who were interested in this distribution. For example: See, [10][11][12][13][14][15][16][17][18][19][20]. In this year some authors study type II Topp-Leone, for example: see, [21,22].…”