Hypothesis test for changes in variance using a statistic based in P-values in a time series of normal independent observations.

The present work proposes a Hypothesis Test to detect a shift in the variance of a series of independent normal observations using a statistic based on the p-values of the F distribution. Since the probability distribution function of this statistic is intractable, critical values were we estimated numerically through extensive simulation. A regression approach was used to simplify the quantile evaluation and extrapolation. The power of the test was simulated using Monte Carlo simulation, and the results were compared with the Chen test (1997) to prove its efficiency. Time series analysts might find the test useful to address homoscedasticity studies were at most one change might be involved.

A pilot study to determine the normal haematological indices for young Malawian adults in Blantyre, Malawi

Aim To determine the distribution of haematological parameters in healthy individuals residing in Blantyre, Malawi. We also examined the effect of sociodemographic and nutritional factors on the haematological variables. Methods We conducted a proof-of-concept cross-sectional study, involving 105 healthy blood donors at Malawi Blood Transfusion Service in Blantyre. Eligible participants were HIV-negative males and females, aged 19 to 35 years, who did not have any evidence of acute or chronic illness, or bloodborne infection. We performed the haematological tests at the Malawi-Liverpool Wellcome Trust laboratory in Blantyre, and the screening tests at Malawi Blood Transfusion Service laboratories. Results Out of 170 consenting healthy volunteers, haematological results were available for 105 participants. The proportions of results which were below the lower limit of the manufacturer’s reference ranges were 35.2% (37/105) for haemoglobin, 15.2% (16/105) for neutrophils, 23.8% (25/105) for eosinophils, and 88.6 % (93/105) for basophils. The proportions of results that were above the upper limit of the manufacturer’s reference ranges were 9.5% (10/105) for platelets and 12.4% (13/105) for monocytes. We also observed that the mean leucocyte and basophil counts were significantly higher in males than females (p = 0.042 and p = 0.015, respectively). There were no statistically significant differences in haematological results observed among different ethnic, age, and body mass index groups. Conclusions Over half of otherwise healthy study participants had at least one abnormal haematological result, using previously established foreign standards. More detailed studies are needed to establish locally relevant normal ranges for different age groups and other demographic characteristics of the Malawian population. This will lead to accurate interpretation of laboratory results.

BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate.