Precise Asymptotics in Wichura's Law of Iterated Logarithm

Let {Xn, n ≥ 1} be a sequence of independent and identically distributed random variables with a common distribution function F = P(X ≤ x) in the domain of attraction of an asymmetric stable law, with index α, 1 < α < 2 and set Sn=∑nK=1XK. We prove                                         limε->0(√ε) ∑n≥3(1/n)P(Sn≤(θα-ε)An )=1/(2√2α), where An = n1/α(log log n)((α-1)/α) θα =(B(α))((α-1)/α) and B(α) = (1 − α)α(α/(1-α)) (cos (πα/2)) (α/α-1

Prevalence of Hypertension and Assessment of "Rule of Halves" in Rural Population of Basavanapura Village, Nanjangud Taluk, South India

Context: World Health Day is celebrated on 7 th April to mark the anniversary of the founding of World Health Organization in 1948. Each year a theme is selected for World Health Day that highlights a priority area of public health concern in the world. The theme for 2013 is on high blood pressure (BP). High BP, if left uncontrolled increases the risk of heart attacks, strokes, and kidney failure. Materials and Methods: A community-based cross-sectional survey was carried out among adults (>18 years) in Basavanapura Village, Nanjangud Taluk using simple random sampling method to study the pattern of BP using the Seventh Report of the Joint National Committee criteria. A total of 447 persons were screened. A total of 223 individuals (90 men and 133 women) were selected by simple random sampling, interviewed, and clinically examined for hypertension. BP of all the study participants was measured using a standardized technique. Statistical Analysis Used: Mean ± standard deviation (continuous data), proportions and percentages (categorical data), Chi-square test (association between age and hypertension) and odds were calculated to see in which age group the risk of hypertension was more. Kruskal-Wallis test was used to test the significant difference of systolic BP and diastolic BP for males and females among age groups. Results: Of the 447 persons surveyed in Basavanpura Village, BP was recorded among 223 individuals. The overall prevalence of hypertension was found to be 36 (16.1%), of which 22 (61.1%) were diagnosed, 20 (90.90%) treated, and only 14 (70.0%) controlled. Increasing age, sedentary lifestyles, and male sex were identified as the predisposing factors. Conclusions: The prevalence of hypertension in the village is slightly higher (16.14%) than the national prevalence (14%). There is an urgent need to educate the people to modify the lifestyle and to monitor their BP values regularly