{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:57:57Z","timestamp":1760057877496,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T00:00:00Z","timestamp":1740528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a new bivariate mixture Lindley power function (BMLPF) distribution that employs a conditional approach with non-identical asymmetric distributions, distinguishing itself by the incorporation of a functional shape parameter. Various structural properties of bivariate distribution are presented, including explicit marginals, cumulative distribution function (CDF), product moments, correlation coefficients, conditional densities, moment generating functions, conditional mean, and variances. The parameters of the proposed distribution are evaluated using the maximum likelihood estimation method. To assess the effectiveness of this estimation approach, an extensive simulation study is carried out. The analysis quantifies these point estimators with their standard errors, RMSE, LCL, and UCL. This research significantly contributes to the development and application of bivariate distributions particularly in modeling and analyzing various types of data.<\/jats:p>","DOI":"10.3390\/sym17030353","type":"journal-article","created":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T06:15:33Z","timestamp":1740550533000},"page":"353","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Construction of a New Bivariate Mixture Lindley Power Function Distribution with Functional Shape Parameter Utilizing Non-Identical Distributions via Conditional Approach"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-6059-0411","authenticated-orcid":false,"given":"Arfa","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5591-9511","authenticated-orcid":false,"given":"Muhammad","family":"Ismail","sequence":"additional","affiliation":[{"name":"Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4197-471X","authenticated-orcid":false,"given":"Muhammad","family":"Farooq","sequence":"additional","affiliation":[{"name":"Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"207","DOI":"10.2307\/2983603","article-title":"Sampling from batches","volume":"1","author":"McKay","year":"1934","journal-title":"Suppl. J. R. Stat. Soc."},{"key":"ref_2","first-page":"768","article-title":"On a Characterization of Multivariate Distribution by a Set of Its Conditional Distributions","volume":"41","author":"Patil","year":"1965","journal-title":"Bull. Int. Stat. Inst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1111\/j.2517-6161.1974.tb00999.x","article-title":"Spatial interaction and the statistical analysis of lattice systems","volume":"36","author":"Besag","year":"1974","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1080\/03610928408828690","article-title":"A note on the characterization of bivariate densities by conditional densities","volume":"13","author":"Abrahams","year":"1984","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_5","first-page":"59","article-title":"Bivariate distributions with normal conditionals","volume":"2","author":"Castillo","year":"1987","journal-title":"Proc. Int. Assoc. Sci. Technol. Dev."},{"key":"ref_6","first-page":"233","article-title":"Pseudolikelihood estimation: Some examples","volume":"53","author":"Arnold","year":"1991","journal-title":"Sankhy\u0101 Indian J. Stat. Ser. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"348","DOI":"10.2307\/1270041","article-title":"Shorter Communication: Inferences on the Shape Parameter of a Gamma Distribution: A Conditional Approach","volume":"34","author":"Wong","year":"1992","journal-title":"Technometrics"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lai, C.D., and Balakrishnan, N. (2009). Continuous Bivariate Distributions, Springer.","DOI":"10.1007\/b101765"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1007\/s00477-011-0529-x","article-title":"On the performance of a new bivariate pseudo Pareto distribution with application to drought data","volume":"26","author":"Mohsin","year":"2012","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_10","first-page":"239","article-title":"On some new bivariate pseudo-Gamma distribution","volume":"18","author":"Mohsin","year":"2010","journal-title":"J. Appl. Stat. Sci."},{"key":"ref_11","unstructured":"Amarasekara, S. (2014). A New Bivariate Distribution with Applications, The University of Texas at El Paso."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3025","DOI":"10.1080\/02664763.2020.1793307","article-title":"A new bivariate Poisson distribution via conditional specification: Properties and applications","volume":"48","author":"Ghosh","year":"2021","journal-title":"J. Appl. Stat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.insmatheco.2023.08.005","article-title":"Bivariate distribution regression with application to insurance data","volume":"113","author":"Wang","year":"2023","journal-title":"Insur. Math. Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1080\/01621459.2021.1996379","article-title":"Modeling the extremes of bivariate mixture distributions with application to oceanographic data","volume":"118","author":"Tendijck","year":"2023","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1111\/j.2517-6161.1958.tb00278.x","article-title":"Fiducial distributions and Bayes\u2019 theorem","volume":"20","author":"Lindley","year":"1958","journal-title":"J. R. Stat. Society. Ser. B (Methodol.)"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Lindley, D. (1965). Introduction to Probability and Statistics from a Bayesian Viewpoint, Part 1: Probability, Cambridge University Press.","DOI":"10.1017\/CBO9780511662973"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3844\/jmssp.2015.1.6","article-title":"Bivariate Poisson-Lindley distribution with application","volume":"11","author":"Zamani","year":"2015","journal-title":"J. Math. Stat."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"132","DOI":"10.19139\/soic.v4i2.183","article-title":"Morgenstern type bivariate Lindley distribution","volume":"4","author":"Vaidyanathan","year":"2016","journal-title":"Stat. Optim. Inf. Comput."},{"key":"ref_19","first-page":"25","article-title":"Estimation of Parameters of morgenstern type bivariate lindley distribution by ranked set sampling","volume":"12","author":"Irshad","year":"2019","journal-title":"Istat. J. Turk. Stat. Assoc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s42519-020-00093-9","article-title":"A new bivariate distribution with Rayleigh and Lindley distributions as marginals","volume":"14","author":"Thomas","year":"2020","journal-title":"J. Stat. Theory Pract."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107528","DOI":"10.1016\/j.ress.2021.107528","article-title":"A new class of bivariate Lindley distributions based on stress and shock models and some of their reliability properties","volume":"211","author":"Oliveira","year":"2021","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1007\/s42519-022-00261-z","article-title":"Bivariate Discrete Poisson\u2013Lindley Distributions","volume":"16","author":"Papageorgiou","year":"2022","journal-title":"J. Stat. Theory Pract."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2328831","DOI":"10.1155\/2022\/2328831","article-title":"On statistical properties of a new bivariate modified Lindley distribution with an application to financial data","volume":"2022","author":"Elhassanein","year":"2022","journal-title":"Complexity"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1515\/ms-2023-0038","article-title":"On the Bivariate Generalized Gamma-Lindley Distribution","volume":"73","author":"Ghorbel","year":"2023","journal-title":"Math. Slovaca"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1016\/0026-2714(95)00053-4","article-title":"The power function distribution: A useful and simple distribution to assess electrical component reliability","volume":"36","author":"Meniconi","year":"1996","journal-title":"Microelectron. Reliab."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"041652","DOI":"10.1155\/MPE\/2006\/41652","article-title":"Reliability for some bivariate exponential distributions","volume":"2006","author":"Nadarajah","year":"2006","journal-title":"Math. Probl. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1080\/01621459.1971.10482228","article-title":"Bivariate failure rate","volume":"66","author":"Basu","year":"1971","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s10260-013-0246-3","article-title":"A new bivariate exponential distribution for modeling moderately negative dependence","volume":"23","author":"Mohsin","year":"2014","journal-title":"Stat. Methods Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0047-259X(75)90055-X","article-title":"A vector multivariate hazard rate","volume":"5","author":"Johnson","year":"1975","journal-title":"J. Multivar. Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1093\/biomet\/65.1.141","article-title":"A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence","volume":"65","author":"Clayton","year":"1978","journal-title":"Biometrika"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1080\/01621459.1989.10478795","article-title":"Bivariate survival models induced by frailties","volume":"84","author":"Oakes","year":"1989","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1080\/01621459.1992.10475263","article-title":"Time-dependent association measures for bivariate survival distributions","volume":"87","author":"Anderson","year":"1992","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.jmva.2013.08.004","article-title":"On bivariate Weibull-geometric distribution","volume":"123","author":"Kundu","year":"2014","journal-title":"J. Multivar. Anal."},{"key":"ref_34","first-page":"1155","article-title":"Inference of bivariate generalized exponential distribution based on copula functions","volume":"11","author":"Jarwan","year":"2017","journal-title":"Appl. Math. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"75","DOI":"10.5539\/mas.v14n6p75","article-title":"Modification of semi-analytical method applied system of ODE","volume":"14","author":"Nave","year":"2020","journal-title":"Mod. Appl. Sci"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.17713\/ajs.v53i1.1551","article-title":"Bivariate Poisson Generalized Lindley Distributions and the Associated BINAR (1) Processes","volume":"53","author":"Rasheed","year":"2024","journal-title":"Austrian J. Stat."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"75","DOI":"10.18187\/pjsor.v14i1.2192","article-title":"A new multivariate Weibull distribution","volume":"14","author":"Shahbaz","year":"2018","journal-title":"Pak. J. Stat. Oper. Res."},{"key":"ref_38","first-page":"32","article-title":"Some distributional properties of the concomitants of record statistics for bivariate pseudo-exponential distribution and characterization","volume":"6","author":"Mohsin","year":"2010","journal-title":"J. Prime Res. Math."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Johnson, R.A., and Wichern, D. (1998). Applied Multivariate Statistical Analysis. Biometrics, 54.","DOI":"10.2307\/2533879"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2609042","DOI":"10.1155\/2022\/2609042","article-title":"Bivariate Kumaraswamy distribution based on conditional hazard functions: Properties and application","volume":"2022","author":"Mohammed","year":"2022","journal-title":"Math. Probl. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/353\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:42:47Z","timestamp":1760028167000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/353"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,26]]},"references-count":40,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030353"],"URL":"https:\/\/doi.org\/10.3390\/sym17030353","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,2,26]]}}}