Classical and Bayesian inference for the new four-parameter Lomax distribution with applications.

In this study, a new four-parameter Lomax distribution is proposed using a new alpha power transformation technique. The new distribution is named "New Alpha Power Transformed Power Lomax Distribution." Mathematical properties, including moments, the moment-generating function, the mean residual life, order statistics, and the quantile function, are obtained. The maximum likelihood estimation approach is used to estimate the model parameters. A comprehensive simulation is used to evaluate the behavior of maximum likelihood estimators. Two real-world data sets were used to demonstrate the significance of the proposed model, and the results show that the new model performs better when interpreting lifetime data sets. In the end, for the data sets, Bayesian estimation and Metropolis-Hasting's approach were also utilized to construct the approximate Bayes estimates, and convergence diagnostic methods based on Markov Chain Monte Carlo techniques were applied.

An exponentiated XLindley distribution with properties, inference and applications.

In this paper, we propose exponentiated XLindley (EXL) distribution. The novel model is adaptable due to the mixt shapes of its density and failure rate functions. The following key statistical properties of EXL distribution are derived: quantile function, moments, hazard function, mean residual life, and Rényi entropy. The parameters are estimated using the maximum likelihood, Anderson Darling, Cramer von Misses, maximum product spacing, ordinary and weighted least square estimation procedures. To examine the behavior of the estimate, Monte Carlo simulation is used. Further Bayesian technique is also utilized to estimate the EXL parameters. The traceplot and Geweke diagnostics are used to track the convergence of simulated processes. The applicability of the EXL distribution is demonstrated by three datasets from different domains such as mortality rate due to COVID-19, precipitation in inches, and failure time for repairable items. The proposed distribution provides efficient results as compared to renowned competitive distributions.

Analysis of Covid-19 data using discrete Marshall-Olkinin Length Biased Exponential: Bayesian and frequentist approach.

The paper presents a novel statistical approach for analyzing the daily coronavirus case and fatality statistics. The survival discretization method was used to generate a two-parameter discrete distribution. The resulting distribution is referred to as the "Discrete Marshall-Olkin Length Biased Exponential (DMOLBE) distribution". Because of the varied forms of its probability mass and failure rate functions, the DMOLBE distribution is adaptable. We calculated the mean and variance, skewness, kurtosis, dispersion index, hazard and survival functions, and second failure rate function for the suggested distribution. The DI index demonstrates that the proposed model can represent both over-dispersed and under-dispersed data sets. We estimated the parameters of the DMOLBE distribution. The behavior of ML estimates is checked via a comprehensive simulation study. The behavior of Bayesian estimates is checked by generating 10,000 iterations of Markov chain Monte Carlo techniques, plotting the trace, and checking the proposed distribution. From simulation studies, it was observed that the bias and mean square error decreased with an increase in sample size. To show the importance and flexibility of DMOLBE distribution using two data sets about deaths due to coronavirus in China and Pakistan are analyzed. The DMOLBE distribution provides a better fit than some important discrete models namely the discrete Burr-XII, discrete Bilal, discrete Burr-Hatke, discrete Rayleigh distribution, and Poisson distributions. We conclude that the new proposed distribution works well in analyzing these data sets. The data sets used in the paper was collected from 2020 year.

A new cubic transmuted power-function distribution: Properties, inference, and applications.

A new three-parameter cubic transmuted power distribution is proposed using the cubic rank transformation. The density and hazard functions of the new distribution provide great flexibility. Some mathematical properties of the new model such as quantile function, moments, dispersion index, mean residual life, and order statistics are derived. The model parameters are estimated using five different estimation methods. A comprehensive simulation study is carried out to understand the behavior of derived estimators and choose the best estimation method. The usefulness of the proposed distribution is illustrated using a real dataset. It is concluded that the proposed distribution is better than some well-known existing distributions.

A new one-parameter discrete probability distribution with its neutrosophic extension: mathematical properties and applications.

Count data modeling's significance and its applicability to real-world occurrences have been emphasized in a number of research studies. The purpose of this work is to introduce a new one-parameter discrete distribution for the modeling of count datasets. Some mathematical properties, such as reliability measures, characteristic function, moment-generating function, and associated measurements, such as mean, variance, skewness, kurtosis, and index of dispersion, have been derived and studied. The nature of the probability mass function and failure rate function has been studied graphically. The model parameter is estimated using renowned maximum likelihood estimation methods. A neutrosophic extension of the new model is also introduced for the modeling of interval datasets. In addition, the proposed distribution's applicability was compared to that of other discrete distributions. The study's findings show that the novel discrete distribution is a very appealing alternative to some other discrete competitive distributions.

A new extension of Poisson distribution for asymmetric count data: theory, classical and Bayesian estimation with application to lifetime data.

Several research investigations have stressed the importance of discrete data analysis and its relevance to actual events. The current work focuses on a new discrete distribution with a single parameter that can be derived using the Poisson mixing technique. The new distribution is named the Poisson Entropy-Based Weighted Exponential Distribution. It is useful for discussing asymmetric "right-skewed" data with "heavy" tails. Its failure rate function can be used to explain situations with increasing failure rates. The statistical properties of the new distribution are expressed explicitly. The proposed model is simple to manage for under-, equal-, and over-dispersed datasets. The model parameters are estimated using the maximum likelihood method. We consider the parameter estimation for the new model based on right-censored data with a cure fraction. One more focus of the present study is the Bayesian estimation of the model parameters. In the end, three real-world dataset examples were utilized to show the value of the new distribution. These applications revealed that the new model outperforms other standard discrete models.

Poisson XLindley Distribution for Count Data: Statistical and Reliability Properties with Estimation Techniques and Inference.

In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties including order statistics, hazard rate function, reversed hazard rate function, mode, factorial moments, probability generating function, moment generating function, index of dispersion, Shannon entropy, Mills ratio, mean residual life function, and associated measures are investigated. All these properties can be expressed in explicit forms. It is found that the new probability mass function can be utilized to model positively skewed data with leptokurtic shape. Moreover, the new discrete distribution is considered a proper tool to model equi- and over-dispersed phenomena with increasing hazard rate function. The distribution parameter is estimated by different six estimation approaches, and the behavior of these methods is explored using the Monte Carlo simulation. Finally, two applications to real life are presented herein to illustrate the flexibility of the new model.

Modeling of COVID-19 Cases in Pakistan Using Lifetime Probability Distributions.

The Coronavirus Disease (COVID-19) is a respiratory disease that caused a large number of deaths all over the world since its outbreak. The World Health Organization (WHO) has declared the outbreak a global pandemic. The understanding of the random process related to the behavior infection of COVID-19 is an important health and economic problem. In the proposed study, we analyze the frequency of daily confirmed cases of COVID-19 using different two-parameter lifetime probability distributions. We consider the data from the period of March 11, 2020, to July 25, 2020, of Pakistan. We consider nine lifetime probability distributions for the analysis purpose and the selection of best fit was carried out using log-likelihood, AIC, BIC, RMSE, and R2 goodness-of-fit measures. Results indicate that Weibull distribution provides generally the best-fit probability distribution.

Nalbuphine prevents haemodynamic response to endotracheal intubation.

OBJECTIVE: To determine the efficacy of nalbuphine in preventing the increase in heart rate and mean arterial pressure in response to laryngoscopy and orotracheal intubation. DESIGN: A comparative trial. PLACE AND DURATION OF STUDY: Department of Anaesthesia, Pakistan Naval Hospital Shifa, Karachi, Pakistan, from January 2001 to January 2002. PATIENTS AND METHODS: Forty healthy patients having general anaesthesia for elective surgery, were selected by convenient sampling to receive either saline [group I (control group); n= 20] or nalbuphine 0.2 mg/kg; (group II; n = 20) as a bolus dose, 5 minutes before laryngoscopy. Double blinding was done as the patient as well as the researcher was not aware of which study drug was being given. Heart rate (HR) and mean arterial pressure (MAP) were measured before induction of anaesthesia (time 1), just after intubation (time 2), then after every minute upto 5 minutes (time 3-7) and after 10 minutes of intubation (time 8). Twenty percent rise in heart rate (HR) and mean arterial pressure (MAP) was considered as significant. Data were analyzed by using SPSS version 10. Student's t-test was used for the significance of parameters at p < 0.05 and analysis of variance test (ANOVA) was interpreted for group analysis of the parameters. RESULTS: There was a significant increase (p <0.05) in heart rate (53.4%) in group I after intubation at time 2 compared with baseline at time 1, as compared to group II (15.5%). The HR gradually decreased during time 3 to 8 but still remained slightly higher than group II. MAP also increased significantly (p <0.05) in group I, at time 2 (43.6%) compared with baseline at time 1 as compared to group II (10.5%). The MAP also gradually decreased during time 3 to 8 but remained on slightly higher level than group II. CONCLUSION: Nalbuphine 0.2 mg/kg prevented a marked rise in heart rate and mean arterial pressure associated with laryngoscopy and orotracheal intubation.

Paramedian technique of spinal anesthesia in elderly patients for hip fracture surgery.

The objective of this study was to observe the success rate, difficulties and complications during the technique of spinal anesthesia through para median approach in elderly frail patients with spinal abnormalities, for femur fracture surgery. Case series study was performed at Pakistan Naval Shifa Hospital, Karachi, Pakistan from August 2002 to July 2003, after approval from Scientific Research Council of the Hospital and consent of the patients. Forty elderly patients with spinal abnormalities, ASA II, age 88+/- 8 years, weight 68.5+/-3.5 kg, declared high-risk for anesthesia, scheduled for femur fracture surgery under spinal anesthesia, were selected for study after failure of lumbar puncture (LP) through midline approach at L3-4 or L4-5 level. First routine LP was performed, if failed, then second LP through para median approach was attempted. The success rate of the para median approach was 100%. In 4 patients (10%) there was bloody tap and LP was done after selecting another space or re-adjusting the needle in the same space. Forty percent patients felt paraesthesia during the advancement of spinal needle into the sub-arachnoid space. In conclusion, in the elderly frail patients with spinal deformity, declared high-risk for general anesthesia and where lumbar puncture through midline approach fails due to spinal abnormalities, para median route is an alternate safe approach with success rate of 100%.