Brazilian Journal of Biometrics

The Gamma-Akash probability Model for Survival Analysis of Cancer Patients

2024-07-25T10:26:21-03:00

The search for a suitable probability models for the survival analysis of cancer patients are really challenging because survival times of cancer patients are stochastic in nature and are highly positively skewed. The classical well-known one parameter and two-parameter probability models rarely provide better fit to survival times of cancer patients. In this paper a compound probability model called gamma-Akash distribution, which is a compounding of gamma and Akash distribution, has been proposed for the modeling of survival times of cancer patients. Many important properties of the suggested distribution including its shape, moments (negative moments), hazard function, reversed hazard function, quantile function have been discussed. Method of maximum likelihood has been used to estimate its parameters. A simulation study has been conducted to know the consistency of maximum likelihood estimators. Two real datasets, one relating to acute bone cancer and the other relating to head and neck cancer, has been considered to examine the applicability, suitability and flexibility of the proposed distribution. The goodness of fit of the proposed distribution shows quite satisfactory fit over other considered distributions.

Advanced Optional Randomized Response Models For Mean Estimation Under Non-Response And Measurement Error

2024-05-07T17:25:42-03:00

A regression estimator for estimating the population mean of sensitive variable(s) in the presence of non-response and measurement error simultaneously using two scrambling variables are introduced. Comparisons are made with the mean squared error of the proposed estimator with some of the commonly used estimators i.e. Hansen and Hurwitz estimator, linear regression estimator and Diana et al. estimator. Under large sample approximation, their biases and mean square errors are estimated. In addition, an extensive simulation study with real and hypothetical population are also conducted to evaluate the performance of proposed estimator which show that these estimators perform better than the other considered estimators. A graphically representations are also used to represent the simulation results.

Mathematical Modeling and Performance Optimization of Stock Preparation Unit in Paper Manufacturing Plants using GA and PSO

2024-08-23T14:41:36-03:00

The prominent objective of present study is to develop an efficient mathematical model for performance optimization of stock preparation unit of paper plants using the concept of redundancy. Stock preparation in paper manufacturing involves converting raw stock into finished stock for the paper machine. This process involves several subsystems like storage tanks, repulping/Slushing, deflaking, storage and mixing chests, and the paper machine itself in various redundancy strategies. For the system performance analysis, a mathematical model is developed using Markov birth death process along with reliability, availability, maintainability and dependability (RAMD) investigation of components. The Chapman-Kolmogorov differential-difference equations derived under the exponential behavior of failure and repair rates. The prediction of prominent system effectiveness measure is made using genetic algorithm and particle swarm optimization at various population sizes. Decision matrices are derived for a particular value of parameters. It is observed that predicted optimal availability of stock preparation unit is 0.9207 at a population size of 2500 after 80 iterations. It is revealed that genetic algorithm outperformed over particle swarm optimization in availability prediction of stock preparation unit. The derived results are helpful for system designers and maintenance personnel for effective decision-making for plant operations.

The Poisson-Rama distribution with properties and applications to model over-dispersed count data

2024-09-11T15:59:02-03:00

The discrete data available in any fields of knowledge is influenced by several known and unknown factors and the factors which affect the discrete data are stochastic in nature. The stochastic nature of discrete data is really a challenge for statistician to model and analyse with the existing discrete distributions. In the present paper, Poisson-Rama distribution, a Poisson mixture of Rama distribution, has been proposed to model over-dispersed data. Distributional properties, estimation of parameter using maximum likelihood method, and applications of the proposed distributions have been discussed. The simulation study has been carried out to know the consistency of maximum likelihood estimates of parameter. It is observed that the proposed distribution gives much closure fit than several over-dispersed one parameter discrete distributions including Poisson-Lindley distribution, Poisson-Akash distribution and Poisson-Ishita distribution.

A Probabilistic Study of Duration of Post-partum Amenorrhoea in rural Uttar Pradesh

2024-07-01T15:37:00-03:00

The present study introduces a model designed to assess the distribution of post-partum amenorrhea durations through a mixture of two Weibull distribution. The suitability of the model is evaluated by analysing data extracted from a research project funded by the Indian Council for Medical Research (ICMR). The analysis shows that breastfeeding plays a significant role in how long PPA lasts, with longer breastfeeding linked to longer periods without menstruation. Additionally, women with lower socio-economic status and poorer nutrition tend to have longer PPA durations. Using the two Weibull distributions helps capture the different patterns of PPA, providing a detailed understanding of this important health issue.

Exploring Relationships and Inference Methods for Moments of Dual Generalized Order Statistics Derived from the Siddiqui-Dwivedi Distribution

2024-10-31T13:40:02-03:00

In this paper, recurrence relation for single and product moments of dual generalized order statistics (DGOS) from Siddiqui-Dwivedi (SD) distribution are obtained. Furthermore, we provide the minimum variance linear unbiased estimator (MVLUE) of the position and scale parameters of the kth lower record values (LVR) and order statistics (OS) for the distribution under consideration. In the section 4, a characterization result is presented.

Bayesian implementation of Skew-Normal distributions for experimental error in the description of pepper growth

2024-08-23T10:24:39-03:00

The purpose of this work is to implement and compare three types of Skew-Normal distributions together with the Normal submodel for the experimental error through a Bayesian nonlinear modeling of pepper phenotype growth. The posterior means of the parameters were shown to be invariant to the experimental error. The Sahu Skew-Normal error showed evidence of null asymmetry for all growth models. In general, all Skew-Normal distributions presented the highest accuracy ( ) in relation to the Normal error. The problematic points stand out for the computational cost in the millions of MCMC iterations and the limitations of the BUGS language. The Skew-Normal distribution of Azzalini and Fernandéz & Steel modeled the asymmetry of the data and provided the best goodness of fit (DIC) and the best precision ( ) for the Gompertz and Von Bertalanffy model in relation to the Normal error.

Breastfeeding practices among institutionally delivered newborns: a single centre experience

2024-07-25T10:37:53-03:00

With the rise in institutional deliveries, the responsibility of timely initiation and maintaining optimum breastfeeding practices has shifted from families and community health workers to doctors and nursing personnel. According to the National Family Health Survey - 5, there is significant rise in institutional births from 78.9 % to 88.6 % while early initiation of breastfeeding (EIBF) still ranges from 41.6% to 41.8%. The present study aimed to gain insights into the breastfeeding practices among institutionally delivered newborns, and determine the factors affecting it. This was a hospital based analytical cross-sectional study. After obtaining Institutional Ethics Committee approval and written informed consent, 375 postnatal mothers were interviewed within 24 hours of delivery. Breastfeeding practices were recorded and logistic regression analysis was performed to identify the determinants of EIBF and exclusive breastfeeding (EBF). Out of 375 respondents, only 143 mothers (39.2%) followed EIBF. Pre-lacteal feed was given by 112 mothers (30.7%), while EBF was practiced by 197 mothers (54%). On logistic regression analysis, mothers belonging to upper socio-economic status (p=0.001; AOR, 13.31; 95% CI, 2.8-62.5), normal vaginal delivery (p<0.001; AOR, 0.089; 95%CI,0.1-0.2) and multiparous mothers (p=0.006; AOR,2.494; 95% CI 1.3-4.7) were more likely to follow EIBF. Determinants of exclusive breastfeeding observed in this study was health seeking behavior of mothers as reflected through number of antenatal clinics attended (p=0.001; AOR, 5.298; 95%CI 0.3-0.7) and Caesarean delivery (p<0.001; AOR, 0.410; 95% CI, 0.3-0.7). Breastfeeding practices like timely initiation of breastfeeding and exclusive breastfeeding among the institutionally delivered newborns are comparatively low as opposed to the nation’s average value. Socio-economic profile, mode of delivery, parity, and health seeking behaviour of mothers proved to be the significant factors determining the breastfeeding practices. Antenatal counselling needs to be strengthened with identified bottlenecks like primiparous women, economically underprivileged mothers and mothers with caesarean delivery.