We propose a new asymmetric discrete model by combining the uniform and Poisson–Ailamujia distributions using the binomial decay transformation method. The distribution, named the uniform Poisson–Ailamujia, due to its flexibility is a good alternative to the well-known Poisson and geometric distributions for real data applications in public health, biology, sociology, medicine, and agriculture. Its main statistical properties are studied, including the cumulative and hazard rate functions, moments, and entropy. The new distribution is considered to be suitable for modeling purposes; its parameter is estimated by eight classical methods. Three applications to biological data are presented herein.

In this paper, a new discrete distribution called Binomial-Discrete Lindley (BDL) distribution is proposed by compounding the binomial and discrete Lindley distributions. Some properties of the distribution are discussed including the moment generating function, moments and hazard rate function. The estimation of distribution parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square errors. Automobile claim data applications are also presented to see that the new distribution is useful in modelling data.

In this paper, a new modified version of geometric distribution is proposed. The newly introduced model is called transmuted record type geometric (TRTG) distribution. TRTG distribution is a good alternative to the negative binomial, Poisson and geometric distributions in modeling real data encountered in several applied fields. The main statistical properties of the new distribution were obtained. We determined the measures of value at risk and tail value at risk for the TRTG distribution. These measures are important quantities in actuarial sciences for portfolio optimization under uncertainty. The TRTG parameters were estimated via maximum likelihood, moments, proportions, and Bayesian estimation methods, and the simulation results were determined to explore their performance. Furthermore, a new count regression model based on the TRTG distribution was proposed. Four real data applications were adopted to illustrate the applicability of the TRTG distribution and its count regression model. These applications showed empirically that the TRTG distribution outperforms some important discrete models such as the negative binomial, transmuted geometric, discrete Burr, discrete Chen, geometric, and Poisson distributions.

Background: The prediction of high-flow nasal oxygen (HFNO) failure in patients with coronavirus disease-2019 (COVID-19) having acute respiratory failure (ARF) may prevent delayed intubation and decrease mortality. Aims: To define the related risk factors to HFNO failure and hospital mortality Study Design: Retrospective cohort study. Methods: To this study. 85 critically ill patients (>= 18 years) with COVID- I 9 related acute kidney injury who were treated with HFNO were enrolled. Treatment success was defined as the de-escalation of the oxygenation support to the conventional oxygen therapies. HFNO therapy failure was determined as the need for invasive mechanical ventilation or death. The patients were divided into HFNO-failure (HFNO-F) and HFNO-success (HFNO-S) groups. Electronic medical records and laboratory data were screened for all patients. Respiratory rate oxygenation (ROX) index on the first hour and chest computed tomography (CT) severity score were calculated. Factors related to HFNO therapy failure and mortality were defined. Results: This study assessed 85 patients (median age 67 years, 69.4% male) who were divided into two groups as HFNO success (n = 33) and HFNO failure (n = 52). The respiratory rate oxygenation (ROX) was measured at I hour and the computed tomography (CT) score indicated HFNO failure and intubation, with an area under the receiver operating characteristic of 0.695 for the ROX index and 0.628 for the CT score. A ROX index of 15 in the first hour of therapy were the predictors of HFNO failure and intubation. Age. Acute Physiology and Chronic Health Evaluation II score, arterial blood gas findings "(i.e., partial pressure of oxygen [PaO2]. PaO2 [fraction of inspired oxygenYSO(2) [oxygen saturation] ratio)", and D-dimer levels were also associated with HFNO failure; however. based on logistic regression analysis, a calculated ROX on the first hour of therapy of 15 (OR = 2.83, 95% CI = 1.01-7.88, P = 0.001) were the only independent risk factors. In logistic regression analysis, a ROX calculated on the first hour of therapy of 15 (OR 2.83. 95% CI = 1.01-7.88, P = <0.001) were the independent risk factors for the HFNO failure. The intensive care unit and hospital mortality rates were 80.2% and 82.7%, respectively. in the HFNO failure group. Conclusion: The early prediction of HFNO therapy failure is essential considering the high mortality rate in patients with HFNO therapy failure. Using the ROX index and the chest CT severity score combined with the other clinical parameters may reduce mortality. Additionally multi-centre observational studies are needed to define the predictive value of ROX and chest CT score not only for COVID-19 but also other causes of ARF.

In this study, the stress-strength reliability, $R=P(Y