Families of Discrete Circular Distributions with Some Novel Applications

Mardia, Kanti V.; Sriram, Karthik

doi:10.1007/s13171-022-00298-z

Cited by 2 publications

(4 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) Formula (2.3) is deduced in [11, Lemma V.6.1] by integration by parts and the Fubini theorem. With similar technique, (2.4) is obtained in [26,Section 4]; it is also a consequence of [25, Theorem 3.1] with f (x) = x r and g(y) = y s .…”

Section: Population Momentsmentioning

confidence: 76%

“…The Feller alternative expectation formula (2.3) is deduced in [11,Lemma V.6.1]. The alternative covariance formula (2.4) is obtained in [26,Section 4], and it is a generalization of the Hoeffding covariance formula [15, (5.6)]:…”

Section: Population Momentsmentioning

confidence: 99%

“…The second section presents the main results of this work. Before giving the reciprocal versions of inequalities (1.1)-(1.2), we state a lemma with the Feller alternative expectation formula [11, Lemma V.6.1], and the Hoeffding alternative covariance formula [15, (5.6)] and [26,Section 4.]. Also, new extensions for the discrete case are presented.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Moment inequalities for nonnegative random variables

Castañeda-Leyva

2023

PMS

View full text Add to dashboard Cite

We give reciprocal versions of the Sclove et al. and Feller inequalities for moments of nonnegative random variables. Our results apply to any nonnegative random variable. The strongest assumption is that the moments involved must be finite. Thus, the results obtained also hold for any empirical distribution with nonnegative data. These facts allow potential applications in numerical analysis, probability, and statistical inference, among other disciplines. Moreover, the proposed methodology offers an alternative approach to obtain new inequalities and even to improve some known inequalities. For instance, we give new inequalities for the ratio of gamma functions. In this context, we also improve an inequality by Bustoz and Ismail and some cases of inequalities due to Gurland and Dragomir et al. Additionally, we present a new inequality for finite sums of nonnegative or nonpositive numbers. For some cases, this relation improves even the Cauchy-Bunyakovsky-Schwarz inequality.

show abstract

Section: Population Momentsmentioning

confidence: 76%

Section: Population Momentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Moment inequalities for nonnegative random variables

Castañeda-Leyva

2023

PMS

View full text Add to dashboard Cite

show abstract

“…The idea is to sample from a multivariate normal distribution and then transform the sampled multivariate normal variables into variables with other marginal distributions. This approach has a long history in statistics and simulation and can be dated back in 1970s 25,26 . Cario and Nelson (1997) extended the idea to discrete/mixed marginal distributions 24 …”

Section: Methodsmentioning

confidence: 99%

Advancing unanchored simulated treatment comparisons: A novel implementation and simulation study

Ren,

Welton

et al. 2024

Research Synthesis Methods

View full text Add to dashboard Cite

Population‐adjusted indirect comparisons, developed in the 2010s, enable comparisons between two treatments in different studies by balancing patient characteristics in the case where individual patient‐level data (IPD) are available for only one study. Health technology assessment (HTA) bodies increasingly rely on these methods to inform funding decisions, typically using unanchored indirect comparisons (i.e., without a common comparator), due to the need to evaluate comparative efficacy and safety for single‐arm trials. Unanchored matching‐adjusted indirect comparison (MAIC) and unanchored simulated treatment comparison (STC) are currently the only two approaches available for population‐adjusted indirect comparisons based on single‐arm trials. However, there is a notable underutilisation of unanchored STC in HTA, largely due to a lack of understanding of its implementation. We therefore develop a novel way to implement unanchored STC by incorporating standardisation/marginalisation and the NORmal To Anything (NORTA) algorithm for sampling covariates. This methodology aims to derive a suitable marginal treatment effect without aggregation bias for HTA evaluations. We use a non‐parametric bootstrap and propose separately calculating the standard error for the IPD study and the comparator study to ensure the appropriate quantification of the uncertainty associated with the estimated treatment effect. The performance of our proposed unanchored STC approach is evaluated through a comprehensive simulation study focused on binary outcomes. Our findings demonstrate that the proposed approach is asymptotically unbiased. We argue that unanchored STC should be considered when conducting unanchored indirect comparisons with single‐arm studies, presenting a robust approach for HTA decision‐making.

show abstract

Families of Discrete Circular Distributions with Some Novel Applications

Cited by 2 publications

References 25 publications

Moment inequalities for nonnegative random variables

Moment inequalities for nonnegative random variables

Advancing unanchored simulated treatment comparisons: A novel implementation and simulation study

Contact Info

Product

Resources

About