A NEW flexible exponent power family of distributions with biomedical data analysis.

Probability distributions are widely utilized in applied sciences, especially in the field of biomedical science. Biomedical data typically exhibit positive skewness, necessitating the use of flexible, skewed distributions to effectively model such phenomena. In this study, we introduce a novel approach to characterize new lifetime distributions, known as the New Flexible Exponent Power (NFEP) Family of distributions. This involves the addition of a new parameter to existing distributions. A specific sub-model within the proposed class, known as the New Flexible Exponent Power Weibull (NFEP-Wei), is derived to illustrate the concept of flexibility. We employ the well-established Maximum Likelihood Estimation (MLE) method to estimate the unknown parameters in this family of distributions. A simulation study is conducted to assess the behavior of the estimators in various scenarios. To gauge the flexibility and effectiveness of the NFEP-Wei distribution, we compare it with the AP-Wei (alpha power Weibull), MO-Wei (Marshal Olkin Weibull), classical Wei (Weibull), NEP-Wei (new exponent power Weibull), FRLog-Wei (flexible reduced logarithmic Weibull), and Kum-Wei (Kumaraswamy Weibull) distributions by analyzing four distinct biomedical datasets. The results demonstrate that the NFEP-Wei distribution outperforms the compared distributions.

A novel randomized scrambling technique for mean estimation of a finite population.

In recent decades, the randomized response technique has attracted researchers due to its usefulness in sensitive surveys. The randomized response procedure is used for the collection of responses on sensitive issues such as cheating in examination, income earned through illegal sources, expenditure on luxury items, and amount of tax paid, etc. This study introduces a new variant of quantitative randomized response models for use with sample surveys where the variable of interest is quantitative. The properties of a mean estimator based on the new technique have been studied. Further, the combined and separate evaluation metrics for efficiency and privacy level have also been derived and compared with those of the existing methods. Further, a simulation study has been conducted to prove the improvement in the degree of privacy protection and efficiency. The findings reveal that the suggested randomized response technique is not only more efficient than the existing techniques, but also improves the joint measure of efficiency and respondents' privacy, making it preferable over the existing techniques. A real-world example of a sample survey through the suggested model is also presented which illustrates its usefulness in practical surveys on sensitive issues.

An efficient estimator of population variance of a sensitive variable with a new randomized response technique.

In sampling theory, a majority of the available estimators of population variance are designed for use with non-sensitive variables only. Such estimators cannot perform efficiently when the variable of interest is of sensitive nature, such as use of drugs, illegal income, abortion, cheating in examination, the amount of income tax payable, and the violation of rules by employees, etc. In the current literature, the shortage of research studies on variance estimators of a sensitive variable has created a big research gap and a room for improvement in the efficiency of such estimators. In this paper, a new randomized scrambling technique is proposed, along with a new estimator of population variance. The new estimator achieves improvement in efficiency over the available variance estimators. The proposed estimator is designed for use with simple random sampling and uses the information on an auxiliary variable. The improvement in efficiency is shown for different choices of constants. Besides efficiency, improvement in the unified measure of estimator quality is also achieved with the proposed estimator under the new randomized response model.

A comparative study of randomized response techniques using separate and combined metrics of efficiency and privacy.

In social surveys, the randomized response technique can be considered a popular method for collecting reliable information on sensitive variables. Over the past few decades, it has been a common practice that survey researchers develop new randomized response techniques and show their improvement over previous models. In majority of the available research studies, the authors tend to report only those findings which are favorable to their proposed models. They often tend to hide the situations where their proposed randomized response models perform worse than the already available models. This approach results in biased comparisons between models which may influence the decision of practitioners about the choice of a randomized response technique for real-life problems. We conduct a neutral comparative study of four available quantitative randomized response techniques using separate and combined metrics of respondents' privacy level and model's efficiency. Our findings show that, depending on the particular situation at hand, some models may be better than the other models for a particular choice of values of parameters and constants. However, they become less efficient when a different set of parameter values are considered. The mathematical conditions for efficiency of different models have also been obtained.

An improved version of systematic sampling design for use with linear trend data.

In survey sampling, systematic sampling design has attracted survey researchers in recent years due to its simplicity of use. We introduce a modified variant of systematic sampling scheme which improves the efficiency of a recently developed diagonal systematic sampling method. The suggested modification is also found to be more efficient than the other popular sampling designs in circumstances where the units of the population under consideration exhibit an increasing or decreasing perfect or near-perfect linear trend. Moreover, it is observed that the conditions for efficiency are mathematically strong and practically always hold, hence making the suggested sampling design preferable over the available sampling designs.

Giant nonfunctioning adrenocortical carcinoma: a case report and review of the literature.

BACKGROUND: Adrenocortical carcinoma is a rare and aggressive malignancy. Patients usually present early with manifestation of abnormal hormone secretion. However, adrenocortical carcinoma can also be nonfunctioning, and such patients present late with a mass effect or distant metastases. CASE PRESENTATION: We herein report a case of a 30-year-old Sri-Lankan woman who presented with a 3-month history of left flank pain associated with nausea, vomiting, and weight loss. Imaging revealed a large left upper quadrant mass with a 1.8-cm left lung nodule. The differential diagnoses included a left adrenal mass, left upper pole renal mass, and retroperitoneal sarcoma. A functional adrenal work-up revealed no abnormal findings. Surgical excision of the mass was uneventful with no postoperative complications. Pathological analysis revealed a nonfunctioning adrenocortical carcinoma measuring 16 × 14 × 10 cm. To our knowledge, a mass of this size is among the largest nonfunctioning adrenocortical carcinomas reported in the published literature. The investigations and approach to treatment were consistent with those in the published literature. CONCLUSION: Large nonfunctioning adrenocortical carcinomas pose a diagnostic and therapeutic challenge, and most are diagnosed at a late stage. Appropriate imaging and functional work-up of the mass are vital before treatment. Surgical excision is safe, even for large adrenocortical carcinomas; excision in patients with advanced disease has been shown to have the best outcomes.