Frailty Models Under Xgamma Distribution with Application to Survival Data
Ashok Kumar Palanisamy,
Muthukumar Madaswamy
Issue:
Volume 8, Issue 4, July 2023
Pages:
87-93
Received:
26 July 2023
Accepted:
14 August 2023
Published:
31 August 2023
Abstract: Frailty models provide an alternative to proportional hazards models, which are designed to discover the properties of the unobserved heterogeneity in individual risks of disease and death. In spite of this distribution of the frailty is normally assumed to be continuous. In some circumstances, it is appropriate to recollect discrete frailty distributions. Generally, Gamma, Weibull, Exponential, Lognormal, and Log-logistic baseline distributions have fitted with frailty distribution. The Xgamma distribution among a unique finite aggregate of exponential and gamma distribution and allowance for the different shapes of the hazard function. The study aims to fit the above four distributions with the Xgamma baseline distribution and apply them to test popular actual-lifestyles statistics set. The study result revealed that Xgamma with Positive Stable (PS) frailty model is a good choice for the Veterans' Administration Lung Cancer study data set and Xgamma with Log-Normal (LN) frailty model is the best fit for the Culling dairy heifer cow’s data set. Additionally, Xgamma identifies the baseline distribution with the lowest Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) values. The study result proved Xgamma distribution and its extended model for frailty distribution is the possible approach in a real-life time or survival analysis.
Abstract: Frailty models provide an alternative to proportional hazards models, which are designed to discover the properties of the unobserved heterogeneity in individual risks of disease and death. In spite of this distribution of the frailty is normally assumed to be continuous. In some circumstances, it is appropriate to recollect discrete frailty distri...
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Research Article
On Computing the Metric Dimension of the Families of Alternate Snake Graphs
Basma Mohamed,
Mohamed Amin
Issue:
Volume 8, Issue 4, July 2023
Pages:
94-103
Received:
13 September 2023
Accepted:
8 October 2023
Published:
30 October 2023
Abstract: Consider a robot that is trying to determine its current location while navigating a graph-based environment. To know how distant it is from each group of fixed landmarks, it can send a signal. We handle the problem of precisely identifying the minimum number of landmarks needed and their ideal placement to guarantee the robot can always discover itself. The number of landmarks in the graph is its metric dimension, and the collection of nodes on which they are distributed is its metric basis. The smallest group of nodes required to uniquely identify each other node in a graph using shortest path distances is known as the metric dimension of the graph. We consider the NP-hard problem of finding the metric dimension of graphs. A set of vertices B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. The minimum resolving set is called the metric basis and the cardinality of the basis is called the metric dimension of G. Metric dimension has applications in a wide range of areas such as robot navigation, telecommunications, combinatorial optimization, and pharmacocatual chemistry. In this paper, we determine the metric dimension of the family of alternate snake graphs including alternate snake, alternate k-polygonal snake, double alternate triangular snake and triple alternate triangular snake graph.
Abstract: Consider a robot that is trying to determine its current location while navigating a graph-based environment. To know how distant it is from each group of fixed landmarks, it can send a signal. We handle the problem of precisely identifying the minimum number of landmarks needed and their ideal placement to guarantee the robot can always discover i...
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