Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2324935934', 'doi': 'https://doi.org/10.1142/9781860949531_0010', 'title': 'ASYMPTOTIC FORMS AND BOUNDS FOR TAILS OF CONVOLUTIONS OF COMPOUND GEOMETRIC DISTRIBUTIONS, WITH APPLICATIONS', 'display_name': 'ASYMPTOTIC FORMS AND BOUNDS FOR TAILS OF CONVOLUTIONS OF COMPOUND GEOMETRIC DISTRIBUTIONS, WITH APPLICATIONS', 'publication_year': 2002, 'publication_date': '2002-11-01', 'ids': {'openalex': 'https://openalex.org/W2324935934', 'doi': 'https://doi.org/10.1142/9781860949531_0010', 'mag': '2324935934'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1142/9781860949531_0010', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'proceedings-article', '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/A5047248078', 'display_name': 'Jun Cai', 'orcid': 'https://orcid.org/0000-0002-9254-0404'}, 'institutions': [{'id': 'https://openalex.org/I151746483', 'display_name': 'University of Waterloo', 'ror': 'https://ror.org/01aff2v68', 'country_code': 'CA', 'type': 'education', 'lineage': ['https://openalex.org/I151746483']}, {'id': 'https://openalex.org/I4210156386', 'display_name': 'Actua', 'ror': 'https://ror.org/04pcj0h26', 'country_code': 'CA', 'type': 'nonprofit', 'lineage': ['https://openalex.org/I4210156386']}], 'countries': ['CA'], 'is_corresponding': False, 'raw_author_name': 'JUN CAI', 'raw_affiliation_strings': ['Department of Statistics and Actuarial Sciences, University of Waterloo, Ontario, Canada N2L 3G1, Canada'], 'affiliations': [{'raw_affiliation_string': 'Department of Statistics and Actuarial Sciences, University of Waterloo, Ontario, Canada N2L 3G1, Canada', 'institution_ids': ['https://openalex.org/I151746483', 'https://openalex.org/I4210156386']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5091859966', 'display_name': 'José Garrido', 'orcid': 'https://orcid.org/0000-0002-2016-7524'}, 'institutions': [{'id': 'https://openalex.org/I60158472', 'display_name': 'Concordia University', 'ror': 'https://ror.org/0420zvk78', 'country_code': 'CA', 'type': 'education', 'lineage': ['https://openalex.org/I60158472']}], 'countries': ['CA'], 'is_corresponding': False, 'raw_author_name': 'JOSÉ GARRIDO', 'raw_affiliation_strings': ['Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada H4B 1R6, Canada'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada H4B 1R6, Canada', 'institution_ids': ['https://openalex.org/I60158472']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 3, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 2.822, 'has_fulltext': False, 'cited_by_count': 15, 'citation_normalized_percentile': {'value': 0.619938, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 83, 'max': 84}, 'biblio': {'volume': None, 'issue': None, 'first_page': '114', 'last_page': '131'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11830', 'display_name': 'Point processes and geometric inequalities', 'score': 0.7761, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, '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/T11830', 'display_name': 'Point processes and geometric inequalities', 'score': 0.7761, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, '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/T12404', 'display_name': 'Mathematical Approximation and Integration', 'score': 0.7483, 'subfield': {'id': 'https://openalex.org/subfields/2612', 'display_name': 'Numerical Analysis'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.39570987}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.3844686}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1142/9781860949531_0010', 'pdf_url': None, 'source': None, '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': 4, 'referenced_works': ['https://openalex.org/W1969306513', 'https://openalex.org/W1991753520', 'https://openalex.org/W2082987505', 'https://openalex.org/W2086921236'], 'related_works': ['https://openalex.org/W4391375266', 'https://openalex.org/W3002753104', 'https://openalex.org/W2748952813', 'https://openalex.org/W2600246793', 'https://openalex.org/W2142036596', 'https://openalex.org/W2077600819', 'https://openalex.org/W2072657027', 'https://openalex.org/W2061531152', 'https://openalex.org/W2007980826', 'https://openalex.org/W1979597421'], 'abstract_inverted_index': {'Recent': [0, 443], 'Advances': [1, 253, 282, 444], 'in': [2, 102, 121, 254, 283, 445], 'Statistical': [3, 446], 'Methods,': [4], 'pp.': [5], '114-131': [6], '(2002)': [7], 'No': [8], 'AccessASYMPTOTIC': [9], 'FORMS': [10], 'AND': [11], 'BOUNDS': [12], 'FOR': [13], 'TAILS': [14], 'OF': [15, 17], 'CONVOLUTIONS': [16], 'COMPOUND': [18], 'GEOMETRIC': [19], 'DISTRIBUTIONS,': [20], 'WITH': [21], 'APPLICATIONSJUN': [22], 'CAI': [23], 'and': [24, 30, 41, 46, 76, 90, 135, 189, 216, 238, 247, 267, 276, 300, 324, 353, 377, 393, 399, 403, 419, 425, 429], 'JOSÉ': [25, 42], 'GARRIDOJUN': [26], 'CAIDepartment': [27], 'of': [28, 34, 44, 82, 84, 112, 138, 159, 169, 179, 203, 209, 235, 240, 264, 269, 294, 307, 318, 331, 338, 344, 347, 360, 368, 371, 384, 396, 410, 422, 436], 'Statistics': [29], 'Actuarial': [31], 'Sciences,': [32], 'University': [33], 'Waterloo,': [35], 'Ontario,': [36], 'Canada': [37, 40, 52], 'N2L': [38], '3G1,': [39], 'GARRIDODepartment': [43], 'Mathematics': [45], 'Statistics,': [47], 'Concordia': [48], 'University,': [49], 'Montreal,': [50], 'Quebec,': [51], 'H4B': [53], '1R6,': [54], 'Canadahttps://doi.org/10.1142/9781860949531_0010Cited': [55], 'by:12': [56], 'PreviousNext': [57], 'AboutSectionsPDF/EPUB': [58], 'ToolsAdd': [59], 'to': [60, 64, 105, 117, 161], 'favoritesDownload': [61], 'CitationsTrack': [62], 'CitationsRecommend': [63], 'Library': [65], 'ShareShare': [66], 'onFacebookTwitterLinked': [67], 'InRedditEmail': [68], 'Abstract:': [69], 'In': [70, 142], 'this': [71], 'paper,': [72], 'we': [73], 'derive': [74], 'exponential': [75], 'subexponential': [77], 'asymptotic': [78, 174], 'forms': [79], 'for': [80, 93, 146, 206, 232, 261, 291, 315], 'tails': [81, 95], 'convolutions': [83], 'compound': [85, 348, 372], 'geometric': [86, 349, 373], 'distributions.': [87], 'General': [88], 'lower': [89], 'upper': [91], 'bounds': [92, 145, 158], 'the': [94, 118, 122, 147, 157, 162, 177, 207, 233, 236, 262, 265, 292, 316], 'are': [96, 115, 132, 154], 'given,': [97, 155], 'which': [98], 'can': [99], 'be': [100], 'used': [101], 'some': [103, 180], 'cases': [104], 'determine': [106], 'a': [107, 128, 136, 241, 270], 'closer': [108], 'tail': [109], 'approximation.': [110], 'Applications': [111], 'these': [113], 'results': [114, 131], 'given': [116], 'ruin': [119, 148], 'probability': [120, 149], 'classical': [123], 'risk': [124, 164], 'process': [125], 'perturbed': [126], 'by': [127], 'diffusion;': [129], 'previous': [130], 'easily': [133], 'derived': [134], 'theorem': [137], 'Veraverbeke26': [139], 'is': [140], 'generalized.': [141], 'addition,': [143], 'two-sided': [144], 'with': [150, 213, 297, 321], 'large': [151], 'claim': [152], 'sizes': [153], 'extending': [156], 'Dickson10': [160], 'diffusion': [163], 'model.': [165], 'FiguresReferencesRelatedDetailsCited': [166], 'By': [167], '12Convolutions': [168], 'DistributionsJun': [170, 339], 'Cai29': [171], 'September': [172, 341], '2014On': [173], 'equivalence': [175, 392, 418], 'among': [176], 'solutions': [178, 208, 293, 317], 'defective': [181, 210], 'renewal': [182, 211, 295, 319], 'equationsQingwu': [183], 'Gao,': [184], 'Yu': [185], 'Liu,': [186], 'Georgios': [187], 'Psarrakos': [188], 'Yuebao': [190, 245, 274], 'Wang17': [191], 'November': [192], '2013': [193], '|': [194, 221, 252, 281, 305, 329, 358, 382, 408, 434], 'Lithuanian': [195], 'Mathematical': [196], 'Journal,': [197], 'Vol.': [198, 228, 257, 286, 310, 334, 363, 387, 413, 439], '53,': [199], 'No.': [200, 230, 259, 288, 312, 336, 365, 389, 415, 441], '4Equivalent': [201], 'conditions': [202], 'local': [204], 'asymptotics': [205, 290, 314], 'equations,': [212, 296, 320], 'applicationsKai-yong': [214], 'Wang': [215, 246, 275], 'Yue-bao': [217], 'Wang12': [218], 'June': [219], '2010': [220], 'Acta': [222], 'Mathematicae': [223], 'Applicatae': [224], 'Sinica,': [225], 'English': [226], 'Series,': [227], '26,': [229], '3Asymptotics': [231], 'moments': [234, 263], 'overshoot': [237, 266], 'undershoot': [239, 268], 'random': [242, 271], 'walkZhaolei': [243, 272], 'Cui,': [244, 273], 'Kaiyong': [248, 277], 'Wang1': [249, 278], 'July': [250, 279, 303, 327, 356, 380, 406, 432], '2016': [251, 280, 304, 328, 357, 381, 407, 433], 'Applied': [255, 284, 308, 332, 361, 385, 411, 437], 'Probability,': [256, 285, 309, 333, 362, 386, 412, 438], '41,': [258, 287, 364, 388, 414, 440], '02Asymptotics': [260], '2Nonexponential': [289], 'applicationsChuancun': [298, 322], 'Yin': [299, 323], 'Junsheng': [301, 325], 'Zhao14': [302, 326], 'Journal': [306, 330, 359, 383, 409, 435], '43,': [311, 335], '03Nonexponential': [313], '3Convolutions': [337], 'Cai15': [340], '2006On': [342], 'applications': [343, 367], 'residual': [345, 369], 'lifetimes': [346, 370], 'convolutionsGordon': [350, 374], 'E.': [351, 375], 'Willmot': [352, 376], 'Jun': [354, 378], 'Cai14': [355, 379], '03On': [366], '3On': [390], 'max-sum': [391, 417], 'convolution': [394, 420], 'closure': [395, 421], 'heavy-tailed': [397, 423], 'distributions': [398, 424], 'their': [400, 426], 'applicationsJun': [401, 427], 'Cai': [402, 428], 'Qihe': [404, 430], 'Tang14': [405, 431], '01On': [416], '1': [442], 'MethodsMetrics': [447], 'History': [448], 'PDF': [449], 'download': [450]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2324935934', 'counts_by_year': [{'year': 2014, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 1}], 'updated_date': '2024-12-13T21:59:19.660739', 'created_date': '2016-06-24'}