Reliability Estimation for a Component Exposed Two, Three Independent Stresses Based on Weibull and InversLindley Distribution

The reliability function for a component which has strength  independently exposed two stresses ; , also when exposed three stresses;    using Weibull distribution with unknown scale and known shape parameters ,and using Invers Lindley distribution  . Estimate the reliability ,  for Weibull distribution by four methods (MLE,MOM,LSE and WLSE) and also in the numerical simulation study a comparison between the four estimates by MES ,MAPE are introduced.   Keywords: Weibull , Invers Lindley  distribution , stress-strength,  reliability estimation, MLE, MOM , LSE and WLS estimation

The dynamic nature of refugee children's resilience: a cohort study of Syrian refugees in Lebanon.

AIMS: Children's responses to war and displacement are varied; many struggle, while others appear resilient. However, research into these outcomes disproportionately focuses on cross-sectional data in high-income countries. We aimed to (1) investigate change in resilience across two timepoints in a highly vulnerable sample of Syrian refugee children in Lebanon, and (2) explore predictors of their mental health problems across time. METHODS: In total, 982 Syrian child-caregiver dyads living in refugee settlements in Lebanon completed questionnaires via interview at baseline and follow-up one year later. We categorised children into groups based on their risk for mental health problems across both timepoints (stable high risk/SHR, deteriorating, improving, stable low risk) according to locally validated cut-offs on measures of post-traumatic stress disorder (PTSD), depression and behavioural problems. Analyses of covariance identified how the groups differed on a range of individual and socio-environmental predictors, followed up by cross-lagged panel models (CLPMs) to investigate the directionality of the relationships between significantly related predictors and symptoms. RESULTS: The sample showed a meaningful amount of change in mental health symptoms from baseline to follow-up. Over half (56.3%) of children met SHR criteria and 10.3% deteriorated over time, but almost one-quarter (24.2%) showed meaningful improvement, and 9.2% were consistently at low risk for mental health problems at both timepoints. Several predictors differentiated the groups, particularly social measures. According to CLPMs, maternal acceptance (β = -0.07) predicted child mental health symptoms over time. Self-esteem (β = -0.08), maternal psychological control (β = 0.10), child maltreatment (β = 0.09) and caregiver depression (β = 0.08) predicted child symptoms and vice versa (βse = -0.11, βb = 0.07, βmpc = 0.08, βcm = 0.1, βcd = 0.11). Finally, child symptoms predicted loneliness (β = 0.12), bullying (β = 0.07), perceived social support (β = -0.12), parent-child conflict (β = 0.13), caregiver PTSD (β = 0.07), caregiver anxiety (β = 0.08) and the perceived refugee environment (β = -0.09). CONCLUSIONS: Our results show risk and resilience are dynamic, and the family environment plays a key role in children's response to war and displacement. Conversely, children also have a significant impact on the family environment and caregiver's own mental health. Interventions to promote resilience in refugee children should therefore consider family-wide mechanisms

Outcome of Depression and Anxiety After War: A Prospective Epidemiologic Study of Children and Adolescents

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106884/1/jts21895.pd