On the generalization of negative binomial distribution

In this paper we study the distribution of the number of trials required to obtain r successes in a sequence of Bernoulli trials. We consider the conditions under which the above distribution is a negative binomial distribution. In fact, we show that the negative binomial distribution can be derived from dependent Bernoulli random variables. Finally, we consider a certain model in a generalized negative binomial distribution and obtain the expected value of the number of trials required.Dependent trials Binomial distribution Negative binomial distribution Generalized negative binomial distribution

Large Sample Inference on the Ratio of Two Independent Binomial Proportions

The asymptotic distribution for the ratio of sample proportions in two independent bernoulli populations is introduced. The presented method can be used to derive the asymptotic confidence interval and hypothesis testing for the ratio of population proportions. The performance of the new interval is comparable with similar confi- dence intervals in the large sample cases. Then the simulation study is provided to compare our confidence interval with some other methods. The proposed confidence set has a good coverage probability with a shorter lengt

The "Woundosome" Concept and Its Impact on Procedural Outcomes in Patients With Chronic Limb-Threatening Ischemia

This editorial assembles endovascular specialists from diverse clinical backgrounds and nationalities with a global call to address key challenges to enhance revascularization in chronic limb-threatening ischemia (CLTI) patients.- Dedicated below-the-ankle (BTA) angiography and revascularization is underutilized in ischemic foot treatment. Existing guidelines do not address comprehensive BTA vessel analysis. CLTI trials also often lack data on in-line arterial flow to the ischemic lesion and BTA vessel evaluation, hindering outcome assessment.- Dedicated multi-planar angiographic evaluation of the distal microcirculation is key: Direct arterial flow or good-quality collaterals are crucial in influencing wound healing and need to be assessed diligently to the level of the distal ischemic wound territory, termed “woundosome.”- An important primary emphasis of future trials should be on validating technologies and strategies for assessing tissue perfusion before, during, and after revascularization undertaken to heal tissue loss in CLTI patients. This will allow determination of a potentially significant delta in tissue perfusion prior to and following intervention at the “woundosome” level. Once changes in arterial perfusion have been identified as positively correlated to wound healing, these could serve as a much-needed novel primary technical outcome measure for patients with tissue loss undergoing surgical, hybrid, or endovascular revascularization