Publication Information

{'id': 'https://openalex.org/W4206386647', 'doi': 'https://doi.org/10.1002/0471271357.ch4', 'title': 'The Multivariate Normal Distribution', 'display_name': 'The Multivariate Normal Distribution', 'publication_year': 2002, 'publication_date': '2002-02-22', 'ids': {'openalex': 'https://openalex.org/W4206386647', 'doi': 'https://doi.org/10.1002/0471271357.ch4'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/0471271357.ch4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210188905', 'display_name': 'Wiley series in probability and statistics', 'issn_l': '1940-6517', 'issn': ['1940-6517', '1940-6347'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'book series'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'other', 'type_crossref': 'other', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5041079208', 'display_name': 'Alvin C. Rencher', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I100005738', 'display_name': 'Brigham Young University', 'ror': 'https://ror.org/047rhhm47', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I100005738']}], 'countries': ['US'], 'is_corresponding': True, 'raw_author_name': 'Alvin C. Rencher', 'raw_affiliation_strings': ['Brigham Young University, USA'], 'affiliations': [{'raw_affiliation_string': 'Brigham Young University, USA', 'institution_ids': ['https://openalex.org/I100005738']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5041079208'], 'corresponding_institution_ids': ['https://openalex.org/I100005738'], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 1, 'citation_normalized_percentile': {'value': 0.541176, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 57, 'max': 64}, 'biblio': {'volume': None, 'issue': None, 'first_page': '82', 'last_page': '111'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11871', 'display_name': 'Advanced Statistical Methods and Models', 'score': 0.5516, 'subfield': {'id': 'https://openalex.org/subfields/2613', 'display_name': 'Statistics and Probability'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11871', 'display_name': 'Advanced Statistical Methods and Models', 'score': 0.5516, 'subfield': {'id': 'https://openalex.org/subfields/2613', 'display_name': 'Statistics and Probability'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T13307', 'display_name': 'Diverse Scientific and Engineering Research', 'score': 0.4981, 'subfield': {'id': 'https://openalex.org/subfields/2206', 'display_name': 'Computational Mechanics'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/matrix-normal-distribution', 'display_name': 'Matrix normal distribution', 'score': 0.7502505}, {'id': 'https://openalex.org/keywords/univariate', 'display_name': 'Univariate', 'score': 0.70789933}, {'id': 'https://openalex.org/keywords/matrix-t-distribution', 'display_name': 'Matrix t-distribution', 'score': 0.69146216}, {'id': 'https://openalex.org/keywords/univariate-distribution', 'display_name': 'Univariate distribution', 'score': 0.60776615}, {'id': 'https://openalex.org/keywords/multivariate-t-distribution', 'display_name': 'Multivariate t-distribution', 'score': 0.55422896}, {'id': 'https://openalex.org/keywords/multivariate-stable-distribution', 'display_name': 'Multivariate stable distribution', 'score': 0.50830907}, {'id': 'https://openalex.org/keywords/elliptical-distribution', 'display_name': 'Elliptical distribution', 'score': 0.49551547}, {'id': 'https://openalex.org/keywords/normality-test', 'display_name': 'Normality test', 'score': 0.42891866}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7764604}, {'id': 'https://openalex.org/C58501165', 'wikidata': 'https://www.wikidata.org/wiki/Q4820795', 'display_name': 'Matrix normal distribution', 'level': 4, 'score': 0.7502505}, {'id': 'https://openalex.org/C199163554', 'wikidata': 'https://www.wikidata.org/wiki/Q1681619', 'display_name': 'Univariate', 'level': 3, 'score': 0.70789933}, {'id': 'https://openalex.org/C43514536', 'wikidata': 'https://www.wikidata.org/wiki/Q17098779', 'display_name': 'Matrix t-distribution', 'level': 4, 'score': 0.69146216}, {'id': 'https://openalex.org/C177384507', 'wikidata': 'https://www.wikidata.org/wiki/Q1149000', 'display_name': 'Multivariate normal distribution', 'level': 3, 'score': 0.68242866}, {'id': 'https://openalex.org/C161584116', 'wikidata': 'https://www.wikidata.org/wiki/Q1952580', 'display_name': 'Multivariate statistics', 'level': 2, 'score': 0.67733353}, {'id': 'https://openalex.org/C79708077', 'wikidata': 'https://www.wikidata.org/wiki/Q7051753', 'display_name': 'Normal-Wishart distribution', 'level': 4, 'score': 0.6575781}, {'id': 'https://openalex.org/C84181548', 'wikidata': 'https://www.wikidata.org/wiki/Q7893853', 'display_name': 'Univariate distribution', 'level': 3, 'score': 0.60776615}, {'id': 'https://openalex.org/C105795698', 'wikidata': 'https://www.wikidata.org/wiki/Q12483', 'display_name': 'Statistics', 'level': 1, 'score': 0.5655785}, {'id': 'https://openalex.org/C172713675', 'wikidata': 'https://www.wikidata.org/wiki/Q6935144', 'display_name': 'Multivariate t-distribution', 'level': 4, 'score': 0.55422896}, {'id': 'https://openalex.org/C102094743', 'wikidata': 'https://www.wikidata.org/wiki/Q133871', 'display_name': 'Normal distribution', 'level': 2, 'score': 0.5497001}, {'id': 'https://openalex.org/C73791607', 'wikidata': 'https://www.wikidata.org/wiki/Q6935142', 'display_name': 'Multivariate stable distribution', 'level': 5, 'score': 0.50830907}, {'id': 'https://openalex.org/C130545031', 'wikidata': 'https://www.wikidata.org/wiki/Q5365806', 'display_name': 'Elliptical distribution', 'level': 4, 'score': 0.49551547}, {'id': 'https://openalex.org/C33962027', 'wikidata': 'https://www.wikidata.org/wiki/Q1930697', 'display_name': 'Wishart distribution', 'level': 3, 'score': 0.46945375}, {'id': 'https://openalex.org/C185429906', 'wikidata': 'https://www.wikidata.org/wiki/Q1130160', 'display_name': 'Estimator', 'level': 2, 'score': 0.46732202}, {'id': 'https://openalex.org/C65778772', 'wikidata': 'https://www.wikidata.org/wiki/Q12345341', 'display_name': 'Asymptotic distribution', 'level': 3, 'score': 0.45055392}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.450116}, {'id': 'https://openalex.org/C79337645', 'wikidata': 'https://www.wikidata.org/wiki/Q779824', 'display_name': 'Outlier', 'level': 2, 'score': 0.44694942}, {'id': 'https://openalex.org/C85031952', 'wikidata': 'https://www.wikidata.org/wiki/Q3026029', 'display_name': 'Normality test', 'level': 3, 'score': 0.42891866}, {'id': 'https://openalex.org/C38180746', 'wikidata': 'https://www.wikidata.org/wiki/Q1952580', 'display_name': 'Multivariate analysis', 'level': 2, 'score': 0.41311133}, {'id': 'https://openalex.org/C87007009', 'wikidata': 'https://www.wikidata.org/wiki/Q210832', 'display_name': 'Statistical hypothesis testing', 'level': 2, 'score': 0.23203507}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/0471271357.ch4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210188905', 'display_name': 'Wiley series in probability and statistics', 'issn_l': '1940-6517', 'issn': ['1940-6517', '1940-6347'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'book series'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4239491687', 'https://openalex.org/W4233789433', 'https://openalex.org/W2953177245', 'https://openalex.org/W2595784461', 'https://openalex.org/W2367324934', 'https://openalex.org/W2138095650', 'https://openalex.org/W2035175677', 'https://openalex.org/W1992713587', 'https://openalex.org/W1976956023', 'https://openalex.org/W1570411980'], 'abstract_inverted_index': {'Most': [0], 'inferential': [1], 'procedures': [2], 'in': [3, 122, 129, 160], 'the': [4, 9, 21, 53, 66, 76, 90, 144, 147, 150, 158, 161], 'book': [5], 'are': [6, 25, 45, 50, 72, 96, 120, 135, 141], 'based': [7], 'on': [8], 'multivariate': [10, 16, 84, 103, 133], 'normal': [11, 17, 40], 'distribution.': [12], 'The': [13], 'properties': [14], 'of': [15, 36, 56, 65, 78, 105, 109, 117, 149, 155, 157], 'random': [18], 'variables': [19, 37], 'include': [20], 'following:': [22], 'linear': [23], 'functions': [24, 29], 'normal,': [26], 'certain': [27], 'quadratic': [28], 'have': [30], 'a': [31, 39, 57, 83, 106], 'chi-square': [32], 'distribution,': [33, 41], 'any': [34, 42], 'subset': [35], 'has': [38], 'two': [43], 'subvectors': [44], 'independent': [46], 'if': [47], 'their': [48], 'covariances': [49], 'all': [51], 'zero,': [52], 'conditional': [54], 'distribution': [55, 77], 'subvector': [58], 'adjusted': [59], 'for': [60, 98, 126, 153], 'another': [61], 'is': [62, 82], 'normal.': [63], 'Estimates': [64], 'mean': [67], 'vector': [68], 'and': [69, 102, 115, 138, 143, 163], 'covariance': [70], 'matrix': [71], 'given,': [73, 142], 'along': [74], 'with': [75], 'these': [79, 110], 'estimators.': [80], 'There': [81], 'central': [85, 92], 'limit': [86, 93], 'theorem': [87], 'corresponding': [88], 'to': [89], 'univariate': [91, 101, 131], 'theorem.': [94], 'Methods': [95, 125], 'given': [97, 121], 'assessing': [99], 'both': [100], 'normality': [104], 'sample.': [107], 'Some': [108], 'methods': [111], 'involve': [112], 'test': [113], 'statistics,': [114], 'tables': [116], 'critical': [118], 'values': [119], 'Appendix': [123], 'A.': [124], 'detecting': [127], 'outliers': [128], 'either': [130], 'or': [132], 'data': [134], 'discussed.': [136], 'Numerical': [137], 'graphical': [139], 'illustrations': [140], 'problems': [145], 'at': [146], 'end': [148], 'chapter': [151, 162], 'call': [152], 'derivation': [154], 'some': [156], 'results': [159], 'provide': [164], 'additional': [165], 'numerical': [166], 'illustrations.': [167]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4206386647', 'counts_by_year': [], 'updated_date': '2024-12-12T07:41:15.831162', 'created_date': '2022-01-25'}