Triangle

Triangle#

The core data structure of the chainladder package

Parameters:

data: DataFrame or DataFrameXchg, or dict: A single dataframe that contains columns representing all other arguments to the Triangle constructor. One may supply a DataFrame-like object (referred to as DataFrameXchg) supporting the __dataframe__ protocol, which will then be converted to a pandas DataFrame. If supplying a dict, it must be structured such that a pandas DataFrame created from it will be accepted by the constructor. If omitted (or if all arguments are omitted), an empty Triangle is returned.
origin: str: Name of the column in data representing the accident, reporting, or more generally the origin period. Maps to the Origin dimension.
development: str: Name of the column in data representing the development or valuation period. Maps to the Development dimension. If omitted, the Triangle is treated as having a single development period (e.g. a latest-diagonal-only view).
columns: str or list: Name(s) of the column(s) in data holding the numeric values that will map to the columns dimension. If omitted, a single 'Total' key is generated.
index: str or list: Name(s) of the column(s) in data that will map to the index dimension. If omitted, a single 'Total' key is generated.
origin_format: str: A string representation of the date format of the origin column (e.g. '%Y-%m-%d'). If omitted, the date format is inferred by pandas.
development_format: str: A string representation of the date format of the development column. If omitted, the date format is inferred by pandas.
cumulative: bool: Whether the triangle is cumulative or incremental. This attribute is required to use the grain and dev_to_val methods and will be automatically set when invoking cum_to_incr or incr_to_cum methods.
trailing: bool, default True: Controls how the period-end month is inferred from origin and development dates. When False, December is treated as the period end (i.e., calendar fiscal periods). When True, the period end is inferred from the data itself. This is useful when origin dates do not align with calendar period boundaries.
array_backend: str, optional (default = None): Backend used to store the underlying values array. One of 'numpy', 'sparse', or 'cupy' (if installed). If None, falls back to cl.options.ARRAY_BACKEND.

Attributes:

index: Series: Represents all available levels of the index dimension.
columns: Series: Represents all available levels of the value dimension.
origin: DatetimeIndex: Represents all available levels of the origin dimension.
development: Series: Represents all available levels of the development dimension.
key_labels: list: Represents the index axis labels
virtual_columns: Series: Represents the subset of columns of the triangle that are virtual.
valuation: DatetimeIndex: Represents all valuation dates of each cell in the Triangle.
origin_grain: str: The grain of the origin vector (‘Y’, ‘S’, ‘Q’, ‘M’)
development_grain: str: The grain of the development vector (‘Y’, ‘S’, ‘Q’, ‘M’)
shape: tuple: The 4D shape of the triangle instance with axes corresponding to (index, columns, origin, development)
link_ratio, age_to_age: Displays age-to-age ratios for the triangle.
valuation_datedate: The latest valuation date of the data
loc: Triangle: pandas-style loc accessor
iloc: Triangle: pandas-style iloc accessor
latest_diagonal: Triangle: The latest diagonal of the triangle
is_cumulative: bool: Whether the triangle is cumulative or not
is_ultimate: bool: Whether the triangle has an ultimate valuation
is_full: bool: Whether lower half of Triangle has been filled in
is_val_tri:: Whether the triangle development period is expressed as valuation periods.
values: array: 4D numpy array underlying the Triangle instance
T: Triangle: Transpose index and columns of object. Only available when Triangle is convertible to DataFrame.

Examples

Constructing a Triangle from a Pandas DataFrame.

import pandas as pd
df = pd.DataFrame(
    data={
        'origin': [1981, 1981, 1981, 1981, 1982, 1982, 1982, 1983, 1983, 1984],
        'development': [1981, 1982, 1983, 1984, 1982, 1983, 1984, 1983, 1984, 1984],
        'reported': [5012, 8269, 10907, 11805, 106, 4285, 5396, 3410, 8992, 5655],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported'],
    cumulative=True,
)
print(tr)

          12      24       36       48
5012.0  8269.0  10907.0  11805.0
 106.0  4285.0   5396.0      NaN
3410.0  8992.0      NaN      NaN
5655.0     NaN      NaN      NaN

When another dimension is added, such as an additional column, the Triangle becomes multidimensional. In this case, printing displays the Triangle’s metadata rather than its contents.

df = pd.DataFrame(
    data={
        'origin': [1981, 1981, 1981, 1981, 1982, 1982, 1982, 1983, 1983, 1984],
        'development': [1981, 1982, 1983, 1984, 1982, 1983, 1984, 1983, 1984, 1984],
        'reported': [5012, 8269, 10907, 11805, 106, 4285, 5396, 3410, 8992, 5655],
        'paid': [2506, 4135, 5454, 5903, 53, 2143, 2698, 1705, 4496, 2828],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported', 'paid'],
    cumulative=True,
)
print(tr)

            Triangle Summary
Valuation:           1984-12
Grain:                  OYDY
Shape:          (1, 2, 4, 4)
Index:               [Total]
Columns:    [reported, paid]

Using the index parameter creates a multi-dimensional Triangle split by a categorical grouping, for example Line of Business.

df = pd.DataFrame(
    data={
         'lob': ['auto', 'auto', 'auto', 'home', 'home', 'home'],
        'origin': [2020, 2020, 2021, 2020, 2020, 2021],
        'development': [2020, 2021, 2021, 2020, 2021, 2021],
        'reported': [100, 150, 80, 200, 280, 160],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported'],
    index=['lob'],
    cumulative=True,
)
print(tr)

           Triangle Summary
Valuation:          2021-12
Grain:                 OYDY
Shape:         (2, 1, 2, 2)
Index:                [lob]
Columns:         [reported]

Non-standard date strings can be parsed by specifying origin_format and development_format using Python strftime codes.

df = pd.DataFrame(
    data={
        'origin': ['2020-01', '2020-01', '2020-02', '2020-02'],
        'development': ['2020-01', '2020-02', '2020-02', '2020-03'],
        'reported': [100, 150, 200, 280],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    origin_format='%Y-%m',
    development='development',
    development_format='%Y-%m',
    columns=['reported'],
    cumulative=True,
)
print(tr)

             1      2   3
2020-01  100.0  150.0 NaN
2020-02  200.0  280.0 NaN
2020-03    NaN    NaN NaN

Setting cumulative=False builds an incremental Triangle, where each cell is the amount accrued within that development period rather than the cumulative total to date.

df = pd.DataFrame(
    data={
        'origin': [1981, 1981, 1981, 1981, 1982, 1982, 1982, 1983, 1983, 1984],
        'development': [1981, 1982, 1983, 1984, 1982, 1983, 1984, 1983, 1984, 1984],
        'reported': [5012, 3257, 2638, 898, 106, 4179, 1111, 3410, 5582, 5655],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported'],
    cumulative=False,
)
print(tr)

          12      24      36     48
5012.0  3257.0  2638.0  898.0
 106.0  4179.0  1111.0    NaN
3410.0  5582.0     NaN    NaN
5655.0     NaN     NaN    NaN

By default (trailing=False), chainladder uses December as the fiscal period end, so origin dates are assigned to calendar quarters. Setting trailing=True instead infers the period end from the data itself, producing quarters aligned to the origin dates.

df = pd.DataFrame(
    data={
        'origin': ['2023-05', '2023-08', '2023-11', '2024-02'],
        'development': ['2024-04', '2024-04', '2024-04', '2024-04'],
        'premium': [100, 130, 160, 140],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    origin_format='%Y-%m',
    development='development',
    development_format='%Y-%m',
    columns=['premium'],
    cumulative=True,
    trailing=False,
)
print(tr)

        2024-04
2023Q2    100.0
2023Q3    130.0
2023Q4    160.0
2024Q1    140.0
2024Q2      NaN

tr = cl.Triangle(
    data=df,
    origin='origin',
    origin_format='%Y-%m',
    development='development',
    development_format='%Y-%m',
    columns=['premium'],
    cumulative=True,
    trailing=True,
)
print(tr)

        2024Q2
2024Q1   100.0
2024Q2   130.0
2024Q3   160.0
2024Q4   140.0

broadcast_axis(axis, value)[source]#

copy()[source]#

cum_to_incr(inplace=False)[source]#

Method to convert an cumlative triangle into a incremental triangle.

Parameters:

inplace: bool: Set to True will update the instance data attribute inplace

Returns:

Updated instance of triangle accumulated along the origin

Examples

cl.load_sample('ukmotor') is a cumulative Triangle. cum_to_incr differences each cell against the prior development period, returning per-period increments.

tr = cl.load_sample('ukmotor')
print(tr.cum_to_incr())

          12      24      36      48      60     72     84
3511.0  3215.0  2266.0  1712.0  1059.0  587.0  340.0
4001.0  3702.0  2278.0  1180.0   956.0  629.0    NaN
4355.0  3932.0  1946.0  1522.0  1238.0    NaN    NaN
4295.0  3455.0  2023.0  1320.0     NaN    NaN    NaN
4150.0  3747.0  2320.0     NaN     NaN    NaN    NaN
5102.0  4548.0     NaN     NaN     NaN    NaN    NaN
6283.0     NaN     NaN     NaN     NaN    NaN    NaN

dev_to_val(inplace=False)[source]#

Converts triangle from a development lag triangle to a valuation triangle.

Parameters:

inplacebool: Whether to mutate the existing Triangle instance or return a new one.

Returns:

Triangle: Updated instance of the triangle with valuation periods.

Examples

cl.load_sample('ukmotor') is a 7x7 cumulative Triangle in development form. Each column represents months of development from the origin year.

tr = cl.load_sample('ukmotor')
print(tr)

          12      24       36       48       60       72       84
3511.0  6726.0   8992.0  10704.0  11763.0  12350.0  12690.0
4001.0  7703.0   9981.0  11161.0  12117.0  12746.0      NaN
4355.0  8287.0  10233.0  11755.0  12993.0      NaN      NaN
4295.0  7750.0   9773.0  11093.0      NaN      NaN      NaN
4150.0  7897.0  10217.0      NaN      NaN      NaN      NaN
5102.0  9650.0      NaN      NaN      NaN      NaN      NaN
6283.0     NaN      NaN      NaN      NaN      NaN      NaN

Calling dev_to_val reshapes the columns from development lags to valuation periods, so each column corresponds to a calendar year.

print(tr.dev_to_val())

        2007    2008    2009     2010     2011     2012     2013
3511.0  6726.0  8992.0  10704.0  11763.0  12350.0  12690.0
   NaN  4001.0  7703.0   9981.0  11161.0  12117.0  12746.0
   NaN     NaN  4355.0   8287.0  10233.0  11755.0  12993.0
   NaN     NaN     NaN   4295.0   7750.0   9773.0  11093.0
   NaN     NaN     NaN      NaN   4150.0   7897.0  10217.0
   NaN     NaN     NaN      NaN      NaN   5102.0   9650.0
   NaN     NaN     NaN      NaN      NaN      NaN   6283.0

development_correlation(p_critical=0.5)[source]#

Mack (1997) test for correlations between subsequent development factors. Results should be within confidence interval range otherwise too much correlation

Parameters:

p_critical: float (default=0.10): Value between 0 and 1 representing the confidence level for the test. A value of 0.1 implies 90% confidence.
Returns
——-: DevelopmentCorrelation object with t, t_critical, t_expectation, t_variance, and range attributes.

Examples

tr = cl.load_sample('raa')
dc = tr.development_correlation()
print(bool(dc.t_critical.iloc[0, 0]))

False

t_critical reports whether the calculated rank correlation falls outside the no-correlation confidence interval. False indicates the development factors are not significantly correlated.

grain(grain='', trailing=False, inplace=False)[source]#

Changes the grain of a cumulative triangle.

Parameters:

grainstr: The grain to which you want your triangle converted, specified as ‘OXDY’ where X and Y can take on values of ['Y', 'S', 'Q', 'M' ] For example, ‘OYDY’ for Origin Year/Development Year, ‘OQDM’ for Origin quarter/Development Month, etc.
trailingbool: For partial origin years/quarters, trailing will set the year/quarter end to that of the latest available from the origin data.
inplacebool: Whether to mutate the existing Triangle instance or return a new one.

Returns:

Triangle

Examples

Build a quarterly origin / quarterly development Triangle (OQDQ).

import pandas as pd

df = pd.DataFrame(
    data={
        'origin': [
            '2022Q1', '2022Q1', '2022Q1', '2022Q1', '2022Q1', '2022Q1', '2022Q1', '2022Q1',
            '2022Q2', '2022Q2', '2022Q2', '2022Q2', '2022Q2', '2022Q2', '2022Q2',
            '2022Q3', '2022Q3', '2022Q3', '2022Q3', '2022Q3', '2022Q3',
            '2022Q4', '2022Q4', '2022Q4', '2022Q4', '2022Q4',
            '2023Q1', '2023Q1', '2023Q1', '2023Q1',
            '2023Q2', '2023Q2', '2023Q2',
            '2023Q3', '2023Q3',
            '2023Q4',
        ],
        'development': [
            '2022Q1', '2022Q2', '2022Q3', '2022Q4', '2023Q1', '2023Q2', '2023Q3', '2023Q4',
            '2022Q2', '2022Q3', '2022Q4', '2023Q1', '2023Q2', '2023Q3', '2023Q4',
            '2022Q3', '2022Q4', '2023Q1', '2023Q2', '2023Q3', '2023Q4',
            '2022Q4', '2023Q1', '2023Q2', '2023Q3', '2023Q4',
            '2023Q1', '2023Q2', '2023Q3', '2023Q4',
            '2023Q2', '2023Q3', '2023Q4',
            '2023Q3', '2023Q4',
            '2023Q4',
        ],
        'reported': [
            100, 200, 300, 400, 480, 540, 580, 600,
            110, 220, 320, 420, 500, 560, 600,
            120, 240, 350, 450, 520, 580,
            130, 250, 370, 470, 540,
            140, 260, 380, 480,
            150, 270, 390,
            160, 280,
            170,
        ],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported'],
    cumulative=True,
)
print(tr)

           3      6      9      12     15     18     21     24
2022Q1  100.0  200.0  300.0  400.0  480.0  540.0  580.0  600.0
2022Q2  110.0  220.0  320.0  420.0  500.0  560.0  600.0    NaN
2022Q3  120.0  240.0  350.0  450.0  520.0  580.0    NaN    NaN
2022Q4  130.0  250.0  370.0  470.0  540.0    NaN    NaN    NaN
2023Q1  140.0  260.0  380.0  480.0    NaN    NaN    NaN    NaN
2023Q2  150.0  270.0  390.0    NaN    NaN    NaN    NaN    NaN
2023Q3  160.0  280.0    NaN    NaN    NaN    NaN    NaN    NaN
2023Q4  170.0    NaN    NaN    NaN    NaN    NaN    NaN    NaN

Convert to annual origin / annual development. Origins are summed within each calendar year and development periods are aggregated to year-end.

print(tr.grain('OYDY'))

          12      24
2022  1090.0  2320.0
2023  1320.0     NaN

Convert origin to annual but keep development quarterly (OYDQ).

print(tr.grain('OYDQ'))

         3      6      9       12      15      18      21      24
2022  100.0  310.0  640.0  1090.0  1500.0  1860.0  2130.0  2320.0
2023  140.0  410.0  810.0  1320.0     NaN     NaN     NaN     NaN

incr_to_cum(inplace=False)[source]#

Method to convert an incremental triangle into a cumulative triangle.

Parameters:

inplace: bool: Set to True will update the instance data attribute inplace

Returns:

Updated instance of triangle accumulated along the origin

Examples

Construct an incremental triangle and accumulate it along the development axis.

df = pd.DataFrame(
    data={
        'origin': [1981, 1981, 1981, 1981, 1982, 1982, 1982, 1983, 1983, 1984],
        'development': [1981, 1982, 1983, 1984, 1982, 1983, 1984, 1983, 1984, 1984],
        'reported': [5012, 3257, 2638, 898, 106, 4179, 1111, 3410, 5582, 5655],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported'],
    cumulative=False,
)
print(tr)

          12      24      36     48
5012.0  3257.0  2638.0  898.0
 106.0  4179.0  1111.0    NaN
3410.0  5582.0     NaN    NaN
5655.0     NaN     NaN    NaN

print(tr.incr_to_cum())

          12      24       36       48
5012.0  8269.0  10907.0  11805.0
 106.0  4285.0   5396.0      NaN
3410.0  8992.0      NaN      NaN
5655.0     NaN      NaN      NaN

By default incr_to_cum returns a new Triangle. Pass inplace=True to mutate the calling Triangle instead.

print(tr.is_cumulative)

False

tr.incr_to_cum(inplace=True)
print(tr.is_cumulative)

True

reindex(columns=None, fill_value=nan)[source]#

set_index(value, inplace=False)[source]#: Sets the index of the Triangle

shift(periods=-1, axis=3)[source]#

Shift elements along an axis by desired number of periods.

Data that falls beyond the existing shape of the Triangle is eliminated and new cells default to zero.

Parameters:

periodsint: Number of periods to shift. Can be positive or negative.
axis{2 or ‘origin’, 3 or ‘development’, None}, default 3: Shift direction.

Returns:

Triangle: updated with shifted elements

Examples

import pandas as pd
df = pd.DataFrame(
    data={
        'origin': [2020, 2020, 2020, 2021, 2021, 2022],
        'development': [2020, 2021, 2022, 2021, 2022, 2022],
        'reported': [100, 200, 300, 110, 220, 120],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported'],
    cumulative=True,
)
print(tr)

         12     24     36
100.0  200.0  300.0
110.0  220.0    NaN
120.0    NaN    NaN

Shift one period along the development axis (the default). Values move right by one column and the leading column is filled with zeros.

print(tr.shift())

       12     24     36
0.0  100.0  200.0
0.0  110.0  220.0
0.0  120.0    NaN

Shift one period along the origin axis. Each origin row’s data moves down by one and the first origin row is zeroed out.

print(tr.shift(periods=-1, axis='origin'))

         12     24     36
  0.0    0.0    0.0
100.0  200.0  300.0
110.0  220.0    NaN

sort_axis(axis)[source]#

Method to sort a Triangle along a given axis

Parameters:

axisint or str: The axis on which to sort. May be specified as an integer (0, 1, 2, 3) or by name ('index', 'columns', 'origin', 'development').

Returns:

Triangle: New Triangle with the requested axis sorted in ascending order.

Examples

Build a Triangle with two columns supplied in non-alphabetical order.

df = pd.DataFrame(
    data={
        'origin': [2020, 2020, 2021, 2021],
        'development': [2020, 2021, 2021, 2021],
        'reported': [100, 200, 110, 110],
        'paid': [50, 100, 60, 60],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported', 'paid'],
    cumulative=True,
)
print(list(tr.columns))

['reported', 'paid']

Sorting on the columns axis returns a new Triangle with columns in alphabetical order.

print(list(tr.sort_axis('columns').columns))

['paid', 'reported']

trend(trend=0.0, axis='origin', start=None, end=None, ultimate_lag=None, **kwargs)[source]#

Allows for the trending of a Triangle object along either a valuation or origin axis. This method trends using days and assumes a years is 365.25 days long.

Parameters:

trendfloat: The annual amount of the trend. Use 1/(1+trend)-1 to detrend.
axisstr (options: [‘origin’, ‘valuation’]): The axis on which to apply the trend
start: date: The start date from which trend should be calculated. If none is provided then the latest date of the triangle is used.
end: date: The end date to which the trend should be calculated. If none is provided then the earliest period of the triangle is used.
ultimate_lagint: If ultimate valuations are in the triangle, optionally set the overall age (in months) of the ultimate to be some lag from the latest non-Ultimate development

Returns:

Triangle: updated with multiplicative trend applied.

Examples

import pandas as pd

df = pd.DataFrame(
    data={
        'origin': [2020, 2020, 2020, 2021, 2021, 2022],
        'development': [2020, 2021, 2022, 2021, 2022, 2022],
        'reported': [100, 200, 300, 110, 220, 120],
    }
)
tr = cl.Triangle(
    data=df,
    origin='origin',
    development='development',
    columns=['reported'],
    cumulative=True,
)
print(tr)

         12     24     36
100.0  200.0  300.0
110.0  220.0    NaN
120.0    NaN    NaN

Apply a 10% annual trend along the origin axis. The latest origin year (2022) is unchanged; older origins are scaled up by 1.10 per year of distance from the latest origin.

print(tr.trend(0.10, axis='origin'))

         12     24     36
121.0  242.0  363.0
121.0  242.0    NaN
120.0    NaN    NaN

Apply a 10% annual trend along the valuation axis instead. The latest diagonal is unchanged and earlier diagonals are scaled up.

print(tr.trend(0.10, axis='valuation'))

         12     24     36
121.0  220.0  300.0
121.0  220.0    NaN
120.0    NaN    NaN

val_to_dev(inplace=False)[source]#

Converts triangle from a valuation triangle to a development lag triangle.

Parameters:

inplacebool: Whether to mutate the existing Triangle instance or return a new one.

Returns:

Updated instance of triangle with development lags

Examples

val_to_dev is the inverse of dev_to_val. Round-tripping a development triangle through valuation form and back returns the original layout.

tr = cl.load_sample('ukmotor')
print(tr.dev_to_val().val_to_dev())

          12      24       36       48       60       72       84
3511.0  6726.0   8992.0  10704.0  11763.0  12350.0  12690.0
4001.0  7703.0   9981.0  11161.0  12117.0  12746.0      NaN
4355.0  8287.0  10233.0  11755.0  12993.0      NaN      NaN
4295.0  7750.0   9773.0  11093.0      NaN      NaN      NaN
4150.0  7897.0  10217.0      NaN      NaN      NaN      NaN
5102.0  9650.0      NaN      NaN      NaN      NaN      NaN
6283.0     NaN      NaN      NaN      NaN      NaN      NaN

valuation_correlation(p_critical=0.1, total=False)[source]#

Mack test for calendar year effect A calendar period has impact across developments if the probability of the number of small (or large) development factors in that period occurring randomly is less than p_critical

Parameters:

p_critical: float (default=0.10): Value between 0 and 1 representing the confidence level for the test
total:: Whether to calculate valuation correlation in total across all years (True) consistent with Mack 1993 or for each year separately (False) consistent with Mack 1997.
Returns
——-: ValuationCorrelation object with z, z_critical, z_expectation and z_variance attributes.

Examples

tr = cl.load_sample('raa')
vc = tr.valuation_correlation()
print(vc.z_critical)

       1982   1983   1984   1985   1986   1987   1988   1989   1990
1981  False  False  False  False  False  False  False  False  False

Each cell of z_critical flags whether the calendar-period z-statistic for that valuation falls outside the no-effect confidence interval. False everywhere means no calendar period shows a significant large-or-small bias on its diagonal.

Inherited Methods

`Triangle.append`	Append rows of other to the end of caller, returning a new object.
`Triangle.astype`	Copy of the array, cast to a specified type.
`Triangle.compute`
`Triangle.cumsum`	Refer to pandas for `cumsum` functionality.
`Triangle.describe`	Refer to pandas for `describe` functionality.
`Triangle.diff`	Refer to pandas for `diff` functionality.
`Triangle.drop`	Drop specified labels from rows or columns.
`Triangle.drop_duplicates`	Refer to pandas for `drop_duplicates` functionality.
`Triangle.dropna`	Method that removes origin/development vectors from edge of a triangle that are all missing values.
`Triangle.exp`
`Triangle.fillna`	Fill nan with 'value' by axis.
`Triangle.fillzero`	Fill nan with 0 by axis.
`Triangle.get_array_module`	Returns the module pertaining to the backend underlying the supplied array.
`Triangle.groupby`	Group Triangle by index values.
`Triangle.head`
`Triangle.heatmap`	Color the background in a gradient according to the data in each column (optionally row).
`Triangle.hvplot`	Passthrough of pandas functionality
`Triangle.log`
`Triangle.max`	Refer to pandas for `max` functionality.
`Triangle.maximum`
`Triangle.mean`	Refer to pandas for `mean` functionality.
`Triangle.median`	Refer to pandas for `median` functionality.
`Triangle.melt`	Refer to pandas for `melt` functionality.
`Triangle.min`	Refer to pandas for `min` functionality.
`Triangle.minimum`
`Triangle.pct_chg`	Refer to pandas for `pct_chg` functionality.
`Triangle.pipe`
`Triangle.pivot`	Refer to pandas for `pivot` functionality.
`Triangle.plot`	Passthrough of pandas functionality
`Triangle.prod`	Refer to pandas for `prod` functionality.
`Triangle.quantile`	Refer to pandas for `quantile` functionality.
`Triangle.rename`	Alter axes labels.
`Triangle.round`
`Triangle.set_backend`	Converts triangle array_backend.
`Triangle.sort_index`
`Triangle.sqrt`
`Triangle.std`	Refer to pandas for `std` functionality.
`Triangle.sum`	Refer to pandas for `sum` functionality.
`Triangle.tail`
`Triangle.to_clipboard`	Refer to pandas for `to_clipboard` functionality.
`Triangle.to_csv`	Refer to pandas for `to_csv` functionality.
`Triangle.to_dict`	Refer to pandas for `to_dict` functionality.
`Triangle.to_excel`	Refer to pandas for `to_excel` functionality.
`Triangle.to_frame`	Converts a triangle to a pandas.DataFrame.
`Triangle.to_html`	Refer to pandas for `to_html` functionality.
`Triangle.to_json`	Serializes triangle object to json format
`Triangle.to_pickle`	Serializes triangle object to pickle.
`Triangle.unstack`	Refer to pandas for `unstack` functionality.
`Triangle.var`	Refer to pandas for `var` functionality.
`Triangle.xs`	Mimics xs from pandas.

Triangle

Contents

Triangle#